Page 1

y = kx + b an . ak = an

+k

an : ak = an

-k

Решение задач

(a n)k = a nk (a - b)(a + b) = a 2 - b 2

Из учебника Ю. Н. Макарычева, Н. Г. Миндюк, К. И. Нешкова, С. Б. Суворовой

«Алгебра. 7 класс»

(a - b) 2 = a 2 - 2ab + b 2

(М.: Просвещение, 2004)

(a + b) 2 = a 2 + 2ab + b 2 a 3 + b 3 = (a + b)(a 2 - ab + b 2) y = kx + b an . ak = an

+k

an : ak = an

-k

(a n)k = a nk (a - b)(a + b) = a 2 - b 2

Москва ОНИКС Мир и Образование 2005


УДК 512(076.2) ББК 22.14 Р47

Автор-составитель Н. Д. Луканов

Решение задач из учебника Ю. Н. Макарычева, Н. Г. МинР47 дюк, К. И. Нешкова, С. Б. Суворовой «Алгебра. 7 класс» / Авт.-сост. Н. Д. Луканов. — М.: ООО «Издательство Оникс»: ООО «Издательство «Мир и Образование», 2005. — 288 с.: ил. ISBN 5-488-00120-4 (ООО «Издательство Оникс») ISBN 5-94666-237-6 (ООО «Издательство «Мир и Образование»)

Пособие содержит решения всех задач из последнего издания учебника Ю. Н. Макарычева, Н. Г. Миндюк, К. И. Нешкова, С. Б. Суворовой «Алгебра. 7 класс», включая и задач и повышенной трудности. Оно будет полезно ученикам и их родителям при проверке домашних заданий и незаменимо в тех случаях, если ученику приходится заниматься самостоятельно. УДК 512(076.2) ББК 22.14 ISBN 5-488-00120-4 (ООО «Издательство Оникс») ISBN 5-94666-237-6 (ООО «Издательство «Мир и Образование») © ООО «Издательство «Мир и Образование», 2005 © Оформление обложки. ООО «Издательство Оникс», 2005


Ãëàâà I ÂÛÐÀÆÅÍÈß, ÒÎÆÄÅÑÒÂÀ, ÓÐÀÂÍÅÍÈß

§ 1. Âûðàæåíèÿ 1. ×èñëîâûå âûðàæåíèÿ 







    

       

      

      

    



   









    



  

   

         

            

  

    ---   

                  

—2—

—3—





    




 

      

    

     

 

  

 

       

   

                

                   

       

 

          













  







    –

–

 -  ------  ---------------------------  ------------  ------  ----    

       



 +   +  -  ------------  ---  ---  ---  ---  --------------------------















   -  ---  ------  ----------------  ------  ---  ----









   ------  ---  -------------------  ---  ---

 ---  ---  







 



      ------  ------  ------  ------  -------------------   ---  ---   













  

   ------  --------------------   ---    

    ------  ---  -------------------   ---  ---   

            



        ---   







 

 ---   --- 

   + ------ ------    ---  ---   –---------------------       –       ---  ---  ------------  ------  ------      

    -  -------------------  ---  ---    ----





 



  -  ---

 ---  ---  ---------------







  ---  ---  ---  ---

—4—



      



  –  –  -  ------------------  ------  ---  ---  --------------------------

                      









    +  +  -  ---------------  ------  ------  ---  ---  --------------------------     

  ------  ------   ------       ---  





 ------  ------    ---  ---  ---   ---    



  +  +  -  -------------------  ------  ------  ---  ---  ---------------------------



—5—








 

      

    

     

 

  

 

       

   

                

                   

       

 

          













  







    –

–

 -  ------  ---------------------------  ------------  ------  ----    

       



 +   +  -  ------------  ---  ---  ---  ---  --------------------------















   -  ---  ------  ----------------  ------  ---  ----









   ------  ---  -------------------  ---  ---

 ---  ---  







 



      ------  ------  ------  ------  -------------------   ---  ---   













  

   ------  --------------------   ---    

    ------  ---  -------------------   ---  ---   

            



        ---   







 

 ---   --- 

   + ------ ------    ---  ---   –---------------------       –       ---  ---  ------------  ------  ------      

    -  -------------------  ---  ---    ----





 



  -  ---

 ---  ---  ---------------







  ---  ---  ---  ---

—4—



      



  –  –  -  ------------------  ------  ---  ---  --------------------------

                      









    +  +  -  ---------------  ------  ------  ---  ---  --------------------------     

  ------  ------   ------       ---  





 ------  ------    ---  ---  ---   ---    



  +  +  -  -------------------  ------  ------  ---  ---  ---------------------------



—5—










  -  -------------  ---  ---  ----





















 





 







  











 

—6—



  ------  ------------------  ---   ---  ---  ---   







  





 ---  --- 

















 ---  ---  ---  ---  --- 

  





-    ---  ---   ---  ---  ----









     ------  -------------------  ---  ---   ---  ---  ---  







   -  ---  ---   ---  ---  ------------







 ---  ---  ---  ---  ---  







  -  ---   ---  ---  ------------













  



-  ------  ------  ------  ----------------------  ---   ---  ---   ---- 















 ---  ---  ---  ---  ---

 + -  ------   ---  ---  ----------







 

-   ---   ---    ---   ----  

  

 – -  ---   ---  ---  -----------



+ 

+  -  ---------------  ------  ---  ---  ------------------ 

 



  -  ---  ---  ---  ------  -----

       

-  ---  ---   ---   -------------------  ------  ---   ---  ---  ---------------





   ---  ---   ---  --- 

 





  ----------------  ------  ---   ---  ---  



  





 

  -  ---  ---  ------   ------  -----

------  ---  ---  ---   







  ------  ---   ---  ---  ---  ---  ---------   

     -   ---  ---   -------------------------





     -  ---  ---------------------------------  ---  ---  ----        



  +  -------------------   ------   ------  ------  ---  ---   

– +  ---  ---  ---  -------------------- --- 



+–   ---  ---  ---  --------------------  

 ---  --- 









  - 

 ---    ---   -------------



   ------   ------  -------------------- ---  ---    ---  --- 







 

-     ---   --------------









 -  ---    ---  ---   ---  -----







 

 – +  -   ---------------------   ---    -------  -------  ------

  

 ---   --------------- 









  ------  ---  ---  ---------------



  

  ------  ---  -------------------  ---  ---   ---  ---  



---  ---  ---  ---

 



  ------  ----------------  ---   ---  --- --- 





 



—7—

– - ------  ---  ---  ----------












  -  -------------  ---  ---  ----





















 





 







  











 

—6—



  ------  ------------------  ---   ---  ---  ---   







  





 ---  --- 

















 ---  ---  ---  ---  --- 

  





-    ---  ---   ---  ---  ----









     ------  -------------------  ---  ---   ---  ---  ---  







   -  ---  ---   ---  ---  ------------







 ---  ---  ---  ---  ---  







  -  ---   ---  ---  ------------













  



-  ------  ------  ------  ----------------------  ---   ---  ---   ---- 















 ---  ---  ---  ---  ---

 + -  ------   ---  ---  ----------







 

-   ---   ---    ---   ----  

  

 – -  ---   ---  ---  -----------



+ 

+  -  ---------------  ------  ---  ---  ------------------ 

 



  -  ---  ---  ---  ------  -----

       

-  ---  ---   ---   -------------------  ------  ---   ---  ---  ---------------





   ---  ---   ---  --- 

 





  ----------------  ------  ---   ---  ---  



  





 

  -  ---  ---  ------   ------  -----

------  ---  ---  ---   







  ------  ---   ---  ---  ---  ---  ---------   

     -   ---  ---   -------------------------





     -  ---  ---------------------------------  ---  ---  ----        



  +  -------------------   ------   ------  ------  ---  ---   

– +  ---  ---  ---  -------------------- --- 



+–   ---  ---  ---  --------------------  

 ---  --- 









  - 

 ---    ---   -------------



   ------   ------  -------------------- ---  ---    ---  --- 







 

-     ---   --------------









 -  ---    ---  ---   ---  -----







 

 – +  -   ---------------------   ---    -------  -------  ------

  

 ---   --------------- 









  ------  ---  ---  ---------------



  

  ------  ---  -------------------  ---  ---   ---  ---  



---  ---  ---  ---

 



  ------  ----------------  ---   ---  --- --- 





 



—7—

– - ------  ---  ---  ----------










        

      





  --------------------    02'33'"    

  ---   ---  ---  ---  ---

  --------------------    02'3'"    

   ---   ---  ---  ---







  

     ---    ---   ---  ---  ---- ----         ---------  ---    ---     ---   ---  ---  ---  

  -#$'"4##5' 

 

                       

   "0-7(%#45%$ % 

 

     !"#$! %  &!'%( %   )!#' %  *%''$ %  +, %  +,-!#'$    % *%''$!'% ' %

 &!'%( %  %,. %  )!#' % %'"'$ '

 *%''$%,. %'  

 

 /  01   /  01   

/  01     /  01         ------------------  



   -   --------------------------









    ---------------------------------  



    ---------------------------------  



  



—8—

  -#.5%#%-6(4' " 

 -------------------- 2 0'%((4%%(% "     

 2   %"%%( 2-4'2.

2. Âûðà æåíèÿ ñ ïåðåìåííûìè  8%     %     %       8%        %         %        

   -   --------------------





    "

    



   -   " 0#%-633%  ------------------------

   

   



   -  "0#%-63%   ---------------------











 











 

















   

   

      

—9—




        

      





  --------------------    02'33'"    

  ---   ---  ---  ---  ---

  --------------------    02'3'"    

   ---   ---  ---  ---







  

     ---    ---   ---  ---  ---- ----         ---------  ---    ---     ---   ---  ---  ---  

  -#$'"4##5' 

 

                       

   "0-7(%#45%$ % 

 

     !"#$! %  &!'%( %   )!#' %  *%''$ %  +, %  +,-!#'$    % *%''$!'% ' %

 &!'%( %  %,. %  )!#' % %'"'$ '

 *%''$%,. %'  

 

 /  01   /  01   

/  01     /  01         ------------------  



   -   --------------------------









    ---------------------------------  



    ---------------------------------  



  



—8—

  -#.5%#%-6(4' " 

 -------------------- 2 0'%((4%%(% "     

 2   %"%%( 2-4'2.

2. Âûðà æåíèÿ ñ ïåðåìåííûìè  8%     %     %       8%        %         %        

   -   --------------------





    "

    



   -   " 0#%-633%  ------------------------

   

   



   -  "0#%-63%   ---------------------











 











 

















   

   

      

—9—


    

    

    

    

     +#%#''. !' '$ ''.6 #.9'5 $#$:%$ -#-9'. % 

  ---   ---     

 ---   ---      

   ---   ---      

 ---   ---       































































 











                                          8%               

                                

                  

   

  

 

  

      ---   ---   



     

— 10 —

        

      

     

 

    

     -  -------  ------  ------  ---  ----------   

–

 – -  -----------   ---------- –

– 

       ---         ---      ---   

 

          ---    

 ---                  2 0%%-#", %   !"#$   % "&"#$ 

      '% "&"#$ ()*+   %( #'%5       ''%5  #

— 11 —


    

    

    

    

     +#%#''. !' '$ ''.6 #.9'5 $#$:%$ -#-9'. % 

  ---   ---     

 ---   ---      

   ---   ---      

 ---   ---       































































 











                                          8%               

                                

                  

   

  

 

  

      ---   ---   



     

— 10 —

        

      

     

 

    

     -  -------  ------  ------  ---  ----------   

–

 – -  -----------   ---------- –

– 

       ---         ---      ---   

 

          ---    

 ---                  2 0%%-#", %   !"#$   % "&"#$ 

      '% "&"#$ ()*+   %( #'%5       ''%5  #

— 11 —


d

S1

S2

c

d

b–c

 

S3 a

            

n

 

 ---



  



  



   -    --------------------------



  ---------------------------   

 

a  )7(-$,"(' ,-(.-"!/*$ ),-%,#,6! '.6%' ;#''$'    %%('4#%   %%(65'"'4   %%(#,656'45

 )!#' 01*/  +, %-!#'$ %    )!#'%,. %  %  &!'%( %-!#'$ %    +,-!#'$ %   %

— 12 —



 '-   

 

 --- 0'4'2'.2''4

)#%6 

,2- ,

 '- 

h





m

S2 S1 y





 )#%6 , &$- ,

x

x–y

  

 +, %'" % %  +,-!#'5''

 )!#'!'% %  '%,, %  

b

        





   -    --------------------------







  

 ---------------------------- 

 /// 0%(-2'#-< 6%$'



   -    -------------------------- 



  .   / / / 0-6%$' %'#

   -  %  ------------------------ 

  --',!#9'.#.-,%( %'#

3. Ã&#x2018;ðà âíåíèå çíà÷åíèé âûðàæåíèé           =    =              =  

Â&#x2014; 13 Â&#x2014;


d

S1

S2

c

d

bâ&#x20AC;&#x201C;c

 

S3 a

            

n

 

 ---



  



  



   -    --------------------------



  ---------------------------   

 

a  )7(-$,"(' ,-(.-"!/*$ ),-%,#,6! '.6%' ;#''$'    %%('4#%   %%(65'"'4   %%(#,656'45

 )!#' 01*/  +, %-!#'$ %    )!#'%,. %  %  &!'%( %-!#'$ %    +,-!#'$ %   %

Â&#x2014; 12 Â&#x2014;



 '-   

 

 --- 0'4'2'.2''4

)#%6 

,2- ,

 '- 

h





m

S2 S1 y





 )#%6 , &$- ,

x

xâ&#x20AC;&#x201C;y

  

 +, %'" % %  +,-!#'5''

 )!#'!'% %  '%,, %  

b

        





   -    --------------------------







  

 ---------------------------- 

 /// 0%(-2'#-< 6%$'



   -    -------------------------- 



  .   / / / 0-6%$' %'#

   -  %  ------------------------ 

  --',!#9'.#.-,%( %'#

3. Ã&#x2018;ðà âíåíèå çíà÷åíèé âûðàæåíèé           =    =              =  

Â&#x2014; 13 Â&#x2014;


  + -  ------   ---  ---  --------------------------



 +   ---  ---  ----------------------------  ------     

      ------ = ------ -1, ---  --- = ---  ---    

 ---  ---  --- ---   ---  --- --- ---  ---  







 --- > ---    --- > --- -1, --- >  ---





     -   ---  ----------------     ---  --------------





-1,  ---   --- 

  =   â&#x20AC;&#x201C; â&#x20AC;&#x201C;  -  ------------------  ------   ---  ---  -------------------------







     ---   ---  ----------  ------ 

 

 



  ------  ------   

  ---------  ---------   

      --------- = --------- -1, --------- > ---------    ---  --- > ---    --- 

       

   â&#x20AC;&#x201C;  

    ----------  --------  ------------------------------  ------ 







  â&#x20AC;&#x201C;

-  ------   ---  ---  -------------------------





      ------ = ------ -1, ---  --- = ---  ------ 

 

  ---  ---  --- =   ---  ---  







     -  ------  ---   ---  ---   ---  ---  ---  ---  -----------















 â&#x20AC;&#x201C; -  ---   ---  ---  ---  ---  -------------------------



 ---  ---  ---    





= --- 



?#'%##'

  >         > ?#'%##'          >-1,  > 

Â&#x2014; 14 Â&#x2014;













   + â&#x20AC;&#x201C;  -  --------  --------  ---------------------  ---  ---   ------ -  ---  ---  ---  ----   







       --- = ------ -1, ---  ---  --- = ---  ---  ---      

 )           =  -1,-  =  )        = -1,-  =  )            =   -1,-  =  )      -1,-  )     =-1,- = )       =  -1,- = )      =  -1, = -  )      -1,  -  )        > -1, >  -  )       >  -1, > -  )      -1,  -  )        =  -1, = -   )     > -1,  > -  )          -1,   -  )           = -1,  = -  )    >  -1, > -  

Â&#x2014; 15 Â&#x2014;


  + -  ------   ---  ---  --------------------------



 +   ---  ---  ----------------------------  ------     

      ------ = ------ -1, ---  --- = ---  ---    

 ---  ---  --- ---   ---  --- --- ---  ---  







 --- > ---    --- > --- -1, --- >  ---





     -   ---  ----------------     ---  --------------





-1,  ---   --- 

  =   â&#x20AC;&#x201C; â&#x20AC;&#x201C;  -  ------------------  ------   ---  ---  -------------------------







     ---   ---  ----------  ------ 

 

 



  ------  ------   

  ---------  ---------   

      --------- = --------- -1, --------- > ---------    ---  --- > ---    --- 

       

   â&#x20AC;&#x201C;  

    ----------  --------  ------------------------------  ------ 







  â&#x20AC;&#x201C;

-  ------   ---  ---  -------------------------





      ------ = ------ -1, ---  --- = ---  ------ 

 

  ---  ---  --- =   ---  ---  







     -  ------  ---   ---  ---   ---  ---  ---  ---  -----------















 â&#x20AC;&#x201C; -  ---   ---  ---  ---  ---  -------------------------



 ---  ---  ---    





= --- 



?#'%##'

  >         > ?#'%##'          >-1,  > 

Â&#x2014; 14 Â&#x2014;













   + â&#x20AC;&#x201C;  -  --------  --------  ---------------------  ---  ---   ------ -  ---  ---  ---  ----   







       --- = ------ -1, ---  ---  --- = ---  ---  ---      

 )           =  -1,-  =  )        = -1,-  =  )            =   -1,-  =  )      -1,-  )     =-1,- = )       =  -1,- = )      =  -1, = -  )      -1,  -  )        > -1, >  -  )       >  -1, > -  )      -1,  -  )        =  -1, = -   )     > -1,  > -  )          -1,   -  )           = -1,  = -  )    >  -1, > -  

Â&#x2014; 15 Â&#x2014;


 )                     -1,    -  )                    >  -1,  >  - )                 = -1,  =  -  )          >  -1, > -      )           =  ?#'%#'#' )            ?#'%#'#' )           >   ?#'%##'   (4 ''(4     (4 ''(4   (4 ''(4   (4''(4 (4 --- ''(4 ---

 --- (4  ''(4  

> > > >   >> > >  >  > >  ?-   

 -  ---  ------   ---  ----  

   ?- -------







------  ?- 



  

------  ---------  ------  ---------    

  --- > -------> ---  

?-  

-  ------   ---  -----

>  > 

> >

  ---  ------  ------      

--- > ------ > ---   

Â&#x2014; 16 Â&#x2014;

 > > >  =

> --- >

>>

  >>  > >

=

b b<a<c

a

c

x

 '(4#'  (4#'  (4#' '(4#' (4#'''(4#' (4#'''(4#' 

(4#' ''(4#' (4#' ''(4#'  )   >  0#' -     0#' -  >  0'#' )    = 0'#' -     0#' -  = 0#' )  0'#' -  0'#' -  0#' -  0#' -  0'#' )   0#' -   0#' -   0#' -   0#' -   0'#'   

 

  >

=

  >  33

 >  

 > 

  

Â&#x2014; 17 Â&#x2014;

 > !


 )                     -1,    -  )                    >  -1,  >  - )                 = -1,  =  -  )          >  -1, > -      )           =  ?#'%#'#' )            ?#'%#'#' )           >   ?#'%##'   (4 ''(4     (4 ''(4   (4 ''(4   (4''(4 (4 --- ''(4 ---

 --- (4  ''(4  

> > > >   >> > >  >  > >  ?-   

 -  ---  ------   ---  ----  

   ?- -------







------  ?- 



  

------  ---------  ------  ---------    

  --- > -------> ---  

?-  

-  ------   ---  -----

>  > 

> >

  ---  ------  ------      

--- > ------ > ---   

Â&#x2014; 16 Â&#x2014;

 > > >  =

> --- >

>>

  >>  > >

=

b b<a<c

a

c

x

 '(4#'  (4#'  (4#' '(4#' (4#'''(4#' (4#'''(4#' 

(4#' ''(4#' (4#' ''(4#'  )   >  0#' -     0#' -  >  0'#' )    = 0'#' -     0#' -  = 0#' )  0'#' -  0'#' -  0#' -  0#' -  0'#' )   0#' -   0#' -   0#' -   0#' -   0'#'   

 

  >

=

  >  33

 >  

 > 

  

Â&#x2014; 17 Â&#x2014;

 > !


--------- @ 0%'$$%%(#$AB",C  

 --------- @ 0%'$$%%(#$AD%# C

   @   @  > +'$$%%(#$AB",C'(4  @   @  =  +'$$%%(#$AB",C(4 

 

        



  



 

§ 2. Ïðåîáðàçîâàíèå âûðàæåíèé



     -------------- / ---------------------------- / ----------- / --------- /  /       



      ----------- / ------------------------- / ------------------------------- / /  



  

    

 

   ------- / ---------------------------------- / /   

      

        



    -------/ --------------------// 

     









    ------------ / ----------------------------- / /0%(-2'#       

'2%%('' / / /    %'2%%(' /

                  

                                                   



 

     

   

— 18 —

4. Ñâîéñòâà äåéñòâèé íàä ÷èñëàìè  )%('%#5%#%9'$ )%('%#5%#,'9'$ + ('%#5%#%9'$ &%-('%#5%#                



                                            

  

                                               + -  --  ---  ---   ----------



-%('% ('%#5%#%9'$

— 19 —


--------- @ 0%'$$%%(#$AB",C  

 --------- @ 0%'$$%%(#$AD%# C

   @   @  > +'$$%%(#$AB",C'(4  @   @  =  +'$$%%(#$AB",C(4 

 

        



  



 

§ 2. Ïðåîáðàçîâàíèå âûðàæåíèé



     -------------- / ---------------------------- / ----------- / --------- /  /       



      ----------- / ------------------------- / ------------------------------- / /  



  

    

 

   ------- / ---------------------------------- / /   

      

        



    -------/ --------------------// 

     









    ------------ / ----------------------------- / /0%(-2'#       

'2%%('' / / /    %'2%%(' /

                  

                                                   



 

     

   

— 18 —

4. Ñâîéñòâà äåéñòâèé íàä ÷èñëàìè  )%('%#5%#%9'$ )%('%#5%#,'9'$ + ('%#5%#%9'$ &%-('%#5%#                



                                            

  

                                               + -  --  ---  ---   ----------



-%('% ('%#5%#%9'$

— 19 —


  + -  ---  -- ---  ---   ----------









-%('% ('%#5%#%9'$   ---  ---  ---  ---    ---  ---     ---  ---     















 ---  ---  ---  ---    ---  ---     ---  ---   



  %$ '#'45  ./-   -/ 4($"($ + ' ------------------------- @ 0%'$$%%(#$  & &+'

    ------  ------  ------  ---  ------   ---  

  ------   ------  ---    ---   ---    



  ---     ---     ---    ---  ---

 ---     ---    ---  





 ---     ---    ---      -    ------    ---   ---  ----  



                                        %$' %#('-!#'< %$' -1,''$%,!%$'             %$ '  %#('  -!#'    %$'-1,''$%,!%$'

Â&#x2014; 20 Â&#x2014;









    ------ 3 ------ 3 ------ (5-" --- 3 --- 3  

                           









 "  #  $ %  

B â&#x20AC;&#x201C;2

D â&#x20AC;&#x201C;1

C 0

A 1

2 x

%"# $ 

5. Ã&#x2019;îæäåñòâà  )%('%#5%#%9'$ + ('%#5%#%9'$ )%('%#5%#%9'$ &%-('%#5%#   )%('%#5%#,'9'$  &%-('%#5%#  )%('%#5%#,'9'$-%(' %#5%#%9'$  + ('%#5%#,'9'$  E#$:%$ E#$:%$ ?$#$:%$ E#$:%$   ?  ?  E  &%-('%#5%# +,-#-9'.6 %#' -!#':" %#'

Â&#x2014; 21 Â&#x2014;


  + -  ---  -- ---  ---   ----------









-%('% ('%#5%#%9'$   ---  ---  ---  ---    ---  ---     ---  ---     















 ---  ---  ---  ---    ---  ---     ---  ---   



  %$ '#'45  ./-   -/ 4($"($ + ' ------------------------- @ 0%'$$%%(#$  & &+'

    ------  ------  ------  ---  ------   ---  

  ------   ------  ---    ---   ---    



  ---     ---     ---    ---  ---

 ---     ---    ---  





 ---     ---    ---      -    ------    ---   ---  ----  



                                        %$' %#('-!#'< %$' -1,''$%,!%$'             %$ '  %#('  -!#'    %$'-1,''$%,!%$'

Â&#x2014; 20 Â&#x2014;









    ------ 3 ------ 3 ------ (5-" --- 3 --- 3  

                           









 "  #  $ %  

B â&#x20AC;&#x201C;2

D â&#x20AC;&#x201C;1

C 0

A 1

2 x

%"# $ 

5. Ã&#x2019;îæäåñòâà  )%('%#5%#%9'$ + ('%#5%#%9'$ )%('%#5%#%9'$ &%-('%#5%#   )%('%#5%#,'9'$  &%-('%#5%#  )%('%#5%#,'9'$-%(' %#5%#%9'$  + ('%#5%#,'9'$  E#$:%$ E#$:%$ ?$#$:%$ E#$:%$   ?  ?  E  &%-('%#5%# +,-#-9'.6 %#' -!#':" %#'

Â&#x2014; 21 Â&#x2014;


  

     

   

  

 ?-     F6!' '5'  E#$%$ ?$#$%$ E#$%$ ?$#$%$  E#$%$ E#$%$ E#$%$ ?$#$%$  

 

     -  ----------------------------     ---   ---   ---------------------





   ---   ---  

-  ------   -------



 

          

 





                 

  -  ------   ----

                                  





   -  ---  -------------------  ------  ------  -----

      -   ---------  ------    ---  ----------------------------

                                      !      !    !

       ---   ---  ---  ---  ---







 )      =  -1, = )         >  -1, > )      > -1, >

6. Ã&#x2019;îæäåñòâåííûå ïðåîáðà çîâàíèÿ âûðàæåíèé                           

Â&#x2014; 22 Â&#x2014;

     

                

      '('('(                 

  

    

 

     

  

    '  '  '

Â&#x2014; 23 Â&#x2014;


  

     

   

  

 ?-     F6!' '5'  E#$%$ ?$#$%$ E#$%$ ?$#$%$  E#$%$ E#$%$ E#$%$ ?$#$%$  

 

     -  ----------------------------     ---   ---   ---------------------





   ---   ---  

-  ------   -------



 

          

 





                 

  -  ------   ----

                                  





   -  ---  -------------------  ------  ------  -----

      -   ---------  ------    ---  ----------------------------

                                      !      !    !

       ---   ---  ---  ---  ---







 )      =  -1, = )         >  -1, > )      > -1, >

6. Ã&#x2019;îæäåñòâåííûå ïðåîáðà çîâàíèÿ âûðàæåíèé                           

Â&#x2014; 22 Â&#x2014;

     

                

      '('('(                 

  

    

 

     

  

    '  '  '

Â&#x2014; 23 Â&#x2014;


                  '   '  '                          

  

  -                -               -           -            ' ' ' ''                      



 ((  ( (  ( - ( ---    ---  



      -  ---     ---       -                 '  ' '  ''                 -1,   --- >  ---

  --- = ---  

 ---  --- = ---  --- >    ---  

                  !! ! !  !                                                 '' ' ' '  - '      

Â&#x2014; 24 Â&#x2014;

-1,

 --- >-1, 

    ---  --- = ---  ---  

 --- > 

   --- > ---      >  

  









    - /    / 0 %( -2'# %'#   ---------------------------------- 

%#.-,%(   //  /  '  /-#.%%$#.-,%%'##%,  A

â&#x20AC;&#x201C;4

E

C

â&#x20AC;&#x201C;2

F 0

BD 2

4 x

% " --- #$ ) --- * 



       

Â&#x2014; 25 Â&#x2014;


                  '   '  '                          

  

  -                -               -           -            ' ' ' ''                      



 ((  ( (  ( - ( ---    ---  



      -  ---     ---       -                 '  ' '  ''                 -1,   --- >  ---

  --- = ---  

 ---  --- = ---  --- >    ---  

                  !! ! !  !                                                 '' ' ' '  - '      

Â&#x2014; 24 Â&#x2014;

-1,

 --- >-1, 

    ---  --- = ---  ---  

 --- > 

   --- > ---      >  

  









    - /    / 0 %( -2'# %'#   ---------------------------------- 

%#.-,%(   //  /  '  /-#.%%$#.-,%%'##%,  A

â&#x20AC;&#x201C;4

E

C

â&#x20AC;&#x201C;2

F 0

BD 2

4 x

% " --- #$ ) --- * 



       

Â&#x2014; 25 Â&#x2014;


§ 3. Ã&#x201C;ðà âíåíèÿ ñ îäíîé ïåðåìåííîé 7. Ã&#x201C;ðàâíåíèå è åãî êîðíè            ),  #' %# #'%# -1,  $#$%$ '''",#''$         *%##'%#'$#$%$#'.-1,'$#$< %$'''",#''$            '$#$%$',#''$

      0''(,#''$

      0''(,#''$

      0'(,#''$

        0''(,#''$            0'(''",#''$

     0'(,#''$

   0''(,#''$

       0''(,#''$

      0'(,#''$    

 0''(,#''$   

 0'(,#''$     0'(,#''$   

 0''(,#''$ G'$''",#''$$#$:%$ %

Â&#x2014; 26 Â&#x2014;

   

  

   ) 9 ! !' '5 #$ %( ,#''$ < 7%$ #    -!#' #' ',: % 6$ . ' ! '95 #'   )1, 9 ! < % $#$%$'''",#''$        )9!!' '5,#''7%$##' %##'%# )1,   $#$:%$'$ ,#''$                            &#'%# #' - :.6 !' '$6 -''5 %< #(' 4' ''" ,#''$ $#$%$ : %        &#'%#'#''-6!' '$6-''5-< 1,'',#''''5           &#'%#'#''-6!' '$6 %#(< ',#''''5        ;#''''(  ?- 

?-  

 ;#'' '$ ;#''''5

;#'''( ;#'' '$

        ;#''$#'%('.:'9' ------   



 

   

 

;#''$#'%('.:'9'         ;#''$#'%('.:'9'

Â&#x2014; 27 Â&#x2014;


§ 3. Ã&#x201C;ðà âíåíèÿ ñ îäíîé ïåðåìåííîé 7. Ã&#x201C;ðàâíåíèå è åãî êîðíè            ),  #' %# #'%# -1,  $#$%$ '''",#''$         *%##'%#'$#$%$#'.-1,'$#$< %$'''",#''$            '$#$%$',#''$

      0''(,#''$

      0''(,#''$

      0'(,#''$

        0''(,#''$            0'(''",#''$

     0'(,#''$

   0''(,#''$

       0''(,#''$

      0'(,#''$    

 0''(,#''$   

 0'(,#''$     0'(,#''$   

 0''(,#''$ G'$''",#''$$#$:%$ %

Â&#x2014; 26 Â&#x2014;

   

  

   ) 9 ! !' '5 #$ %( ,#''$ < 7%$ #    -!#' #' ',: % 6$ . ' ! '95 #'   )1, 9 ! < % $#$%$'''",#''$        )9!!' '5,#''7%$##' %##'%# )1,   $#$:%$'$ ,#''$                            &#'%# #' - :.6 !' '$6 -''5 %< #(' 4' ''" ,#''$ $#$%$ : %        &#'%#'#''-6!' '$6-''5-< 1,'',#''''5           &#'%#'#''-6!' '$6 %#(< ',#''''5        ;#''''(  ?- 

?-  

 ;#'' '$ ;#''''5

;#'''( ;#'' '$

        ;#''$#'%('.:'9' ------   



 

   

 

;#''$#'%('.:'9'         ;#''$#'%('.:'9'

Â&#x2014; 27 Â&#x2014;


     

                                        )         -     -     %  "  #  $ )  * 

y E 1 F D 0

A

B

x

1



C

 

 ---       





                                                                 

   

     

         

 ' --- '







  ---   ---   ---

 ------   ---   



 

   









  ---  

  ---    



 ---  --------- ---  

Â&#x2014; 28 Â&#x2014;





   -     ---      ---   ---  --------------   

 ---  --- 



  ---     --- 

' --- '   --- ' 

------

  

 ---   

                                                    

                       

                       ---

8. Ã&#x2039;èíåéíîå óðà âíåíèå ñ îäíîé ïåðåìåííîé   

   ---  ------   ------

     ---   ---    ---   ---  ---  ---   ---

       -------                   ---   ---    

  ---   --- 

 ---

! --- !

 ---  ---  

 --- !



!

                    

Â&#x2014; 29 Â&#x2014;




     

                                        )         -     -     %  "  #  $ )  * 

y E 1 F D 0

A

B

x

1



C

 

 ---       





                                                                 

   

     

         

 ' --- '







  ---   ---   ---

 ------   ---   



 

   









  ---  

  ---    



 ---  --------- ---  

Â&#x2014; 28 Â&#x2014;





   -     ---      ---   ---  --------------   

 ---  --- 



  ---     --- 

' --- '   --- ' 

------

  

 ---   

                                                    

                       

                       ---

8. Ã&#x2039;èíåéíîå óðà âíåíèå ñ îäíîé ïåðåìåííîé   

   ---  ------   ------

     ---   ---    ---   ---  ---  ---   ---

       -------                   ---   ---    

  ---   --- 

 ---

! --- !

 ---  ---  

 --- !



!

                    

Â&#x2014; 29 Â&#x2014;




                              ------   

 -  -----





 ---  ---  ---  



   ---  ---  ---  



+  --------  --------  ------------  ---  ---     

 ---  ---  

 ---  --- 



 --- 

 ------  ---   ---  ---  ---  ---     

           





  + - --------  ------------  ---  ' ---  ---  --- ' ' --- ' ---  ---  ------



  --- ' ---  --- 





   ---  ---  ------------  --- 

   

' --- 

                              

 ---  ---   ---  ---  

  



  ---  ---  --------- ---  ---     

 --- 

  

              --- 

'' '' ' ' '  '              

 

                

                                               

   

                    

                                                                                              ------             

   ------  ------  ---  



 --- 

             --- 

 

   

           ------  ------        

   

   



   

                                                                                        

                   G'5'

Â&#x2014; 30 Â&#x2014;

Â&#x2014; 31 Â&#x2014;

                                         


                              ------   

 -  -----





 ---  ---  ---  



   ---  ---  ---  



+  --------  --------  ------------  ---  ---     

 ---  ---  

 ---  --- 



 --- 

 ------  ---   ---  ---  ---  ---     

           





  + - --------  ------------  ---  ' ---  ---  --- ' ' --- ' ---  ---  ------



  --- ' ---  --- 





   ---  ---  ------------  --- 

   

' --- 

                              

 ---  ---   ---  ---  

  



  ---  ---  --------- ---  ---     

 --- 

  

              --- 

'' '' ' ' '  '              

 

                

                                               

   

                    

                                                                                              ------             

   ------  ------  ---  



 --- 

             --- 

 

   

           ------  ------        

   

   



   

                                                                                        

                   G'5'

Â&#x2014; 30 Â&#x2014;

Â&#x2014; 31 Â&#x2014;

                                         


          &#'%# #' - : !' '  ,#''  %' ''9%#4'5             G'5'            G'5'                               G'5'                           : %                 G'5'                                                                                               

    

                            

         

          

                                                    

      

Â&#x2014; 32 Â&#x2014;

                                      ---  ---   --- 





                                           ---   --- 



  

     

    

                                                       

 --- 

                                



 ---   ---



                                       

   

 ?-   > > 

   -  ------  ---  ------  ------  ---  ----





 - ?- ---- 







 

------ > ------ > ------    

  - > --- -1, --- > ----





?-  > >   ------  ---  ------  ---   





------  ?-  



   ------ > ------ > ------    

Â&#x2014; 33 Â&#x2014;

------ > --- -1, --- >  






          &#'%# #' - : !' '  ,#''  %' ''9%#4'5             G'5'            G'5'                               G'5'                           : %                 G'5'                                                                                               

    

                            

         

          

                                                    

      

Â&#x2014; 32 Â&#x2014;

                                      ---  ---   --- 





                                           ---   --- 



  

     

    

                                                       

 --- 

                                



 ---   ---



                                       

   

 ?-   > > 

   -  ------  ---  ------  ------  ---  ----





 - ?- ---- 







 

------ > ------ > ------    

  - > --- -1, --- > ----





?-  > >   ------  ---  ------  ---   





------  ?-  



   ------ > ------ > ------    

Â&#x2014; 33 Â&#x2014;

------ > --- -1, --- >  










y

G %#:76

B

A 1 D

0 1

C

x

      -                                  -           

 ),%( '(4$ %'  % " 9$ ! #'.6 9, %5 %' #'     %  ) < ,"('#'          %  -,%#:! #' % +%#,#''           

 

   '(4$ %' #'  %  9$ ! #,6,"60   %  ),%(-#.5 5!"# 5"#5 0   5 H%"'!"#   5 -,%#:#'  $ +%#,#''

              !"#!"!  5 

— 34 —



   

H%"

     

H%"#6266   # -,%#:!<  #'  +%#,#''               #-#26  ###      ##(    # 



D%%"

9. Ðåøåíèå çàäà÷ ñ ïîìîùüþ óðàâíåíèé  ),%(#33%%- #"#3%%-<   # H%"-   # -,%#:! #'  +%#,#''

           

   #33%%- #3%%     #

326 3326 33326

+# J- JI



H%"

    

H%"!%6#  " -,%#:#' " +%#,#''                 '4-,!%6#  "4%'%#0

 "'4I0   " 



G'" 3- 33- 333-





H%"

     

H%"'6-6  '" -,%#:#'  '" +%#,#''             --- 

*% '" 9' .( #.9' ',('. %  --- 0 %'',('  

 %-9''#!9' 

— 35 —






y

G %#:76

B

A 1 D

0 1

C

x

      -                                  -           

 ),%( '(4$ %'  % " 9$ ! #'.6 9, %5 %' #'     %  ) < ,"('#'          %  -,%#:! #' % +%#,#''           

 

   '(4$ %' #'  %  9$ ! #,6,"60   %  ),%(-#.5 5!"# 5"#5 0   5 H%"'!"#   5 -,%#:#'  $ +%#,#''

              !"#!"!  5 

— 34 —



   

H%"

     

H%"#6266   # -,%#:!<  #'  +%#,#''               #-#26  ###      ##(    # 



D%%"

9. Ðåøåíèå çàäà÷ ñ ïîìîùüþ óðàâíåíèé  ),%(#33%%- #"#3%%-<   # H%"-   # -,%#:! #'  +%#,#''

           

   #33%%- #3%%     #

326 3326 33326

+# J- JI



H%"

    

H%"!%6#  " -,%#:#' " +%#,#''                 '4-,!%6#  "4%'%#0

 "'4I0   " 



G'" 3- 33- 333-





H%"

     

H%"'6-6  '" -,%#:#'  '" +%#,#''             --- 

*% '" 9' .( #.9' ',('. %  --- 0 %'',('  

 %-9''#!9' 

— 35 —




@ 0%%(#4' F  -5''.5 -,( '   9  %%# ,#''                %%(#4'#' @

*%' 3$7 33$7 333$7



  



H%"

     

H%" '      - ,%#: #'  +%# ,#''           H-#$7 '##   ' # (   '  !7'#!9' 

K.

+

3, %

,%#

  ,%#

33, %

,%#

  ,%#



+

,@

&

  



)# '$

  





F  -,( -  ':  9   -#  '$  %%#,#''

    

   

          %%#''$%%(-6 @ 

,@

&

+

34'



 

334'





 

Â&#x2014; 36 Â&#x2014;

3"

 #

   #

33"

 #

   #



K.

+

3"

 #

   #

33"

  #

     #

),%#::5%-#', +%#,#''

             #-#5". #



) ':

+

H 3 " !%( '  # (4  +%# ,#''             ##5". #%    ##-#5"%   #

F  ' , %6 ,%# % -#',  %%# ,#''             '#, %.,%#'-#   ,%# 

K.

 ),%('%!-%' % "-#.5, '-,<   #5 0  F!,(-#" #!(4!,(#"%%#,#''

             '%!-%' % 



K.

+

G!'

"

  "

E7

"

"

H !' % #'" (4 '   "  +%# ,#''

              #!'. "#'"

Â&#x2014; 37 Â&#x2014;




@ 0%%(#4' F  -5''.5 -,( '   9  %%# ,#''                %%(#4'#' @

*%' 3$7 33$7 333$7



  



H%"

     

H%" '      - ,%#: #'  +%# ,#''           H-#$7 '##   ' # (   '  !7'#!9' 

K.

+

3, %

,%#

  ,%#

33, %

,%#

  ,%#



+

,@

&

  



)# '$

  





F  -,( -  ':  9   -#  '$  %%#,#''

    

   

          %%#''$%%(-6 @ 

,@

&

+

34'



 

334'





 

Â&#x2014; 36 Â&#x2014;

3"

 #

   #

33"

 #

   #



K.

+

3"

 #

   #

33"

  #

     #

),%#::5%-#', +%#,#''

             #-#5". #



) ':

+

H 3 " !%( '  # (4  +%# ,#''             ##5". #%    ##-#5"%   #

F  ' , %6 ,%# % -#',  %%# ,#''             '#, %.,%#'-#   ,%# 

K.

 ),%('%!-%' % "-#.5, '-,<   #5 0  F!,(-#" #!(4!,(#"%%#,#''

             '%!-%' % 



K.

+

G!'

"

  "

E7

"

"

H !' % #'" (4 '   "  +%# ,#''

              #!'. "#'"

Â&#x2014; 37 Â&#x2014;


 ),%( %% -#" ,!  " " %% #"   "%%(" " D%%-#"(" ,!##%#!(4%%.#" +%# ,#''

              %%-#",!0 "%%#"0   "%%(",!0  "  ),%( %%(  # " .   #  F %#%( #%%#,#''                    %%(   ),%(!'"4#!$ ""!,""#!$ " H'4%%(   "#,"  " F  # 3 4 %%( %6 #  ! (4  %%#,#''                L!34#!$"#'%%( " L!334 #!$"#'%%(  "   # ' 4 %%(  " %6  # ,< " 0 "  F %   % F "     "  F #       #   F $      $ 

y

0

1

x A





   -     ---  --------------------------

   -    ---  ---------------------

 

-   



    – -  ---   ------------     ---    ---  ---   ------  









  -  ---  ---  --------------- ----





 



     ------  ----------------  ------  ---   ---   ---  ---  ---   





 

  -  ---     ----

                >

   =   – -- ---------------- >   + --

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå I



    -  -------------------  ---   ---    ----

M

1



   ---  ---   ---  ---       

Ê ïàðàãðàôó 1

y

A





 





     ------   --------------------  ------  ---  

B

0 1

x N

— 38 —

C

B

 % "

  ---      

 ---   --- >  

D 1

   ---      ---   ---   

 





 -  ---  ---  ---  ----







— 39 —




 ),%( %% -#" ,!  " " %% #"   "%%(" " D%%-#"(" ,!##%#!(4%%.#" +%# ,#''

              %%-#",!0 "%%#"0   "%%(",!0  "  ),%( %%(  # " .   #  F %#%( #%%#,#''                    %%(   ),%(!'"4#!$ ""!,""#!$ " H'4%%(   "#,"  " F  # 3 4 %%( %6 #  ! (4  %%#,#''                L!34#!$"#'%%( " L!334 #!$"#'%%(  "   # ' 4 %%(  " %6  # ,< " 0 "  F %   % F "     "  F #       #   F $      $ 

y

0

1

x A





   -     ---  --------------------------

   -    ---  ---------------------

 

-   



    – -  ---   ------------     ---    ---  ---   ------  









  -  ---  ---  --------------- ----





 



     ------  ----------------  ------  ---   ---   ---  ---  ---   





 

  -  ---     ----

                >

   =   – -- ---------------- >   + --

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå I



    -  -------------------  ---   ---    ----

M

1



   ---  ---   ---  ---       

Ê ïàðàãðàôó 1

y

A





 





     ------   --------------------  ------  ---  

B

0 1

x N

— 38 —

C

B

 % "

  ---      

 ---   --- >  

D 1

   ---      ---   ---   

 





 -  ---  ---  ---  ----







— 39 —






   ---  ---  ---   ---  ---

  

-    ---   --------------------









                                                                       



                                               ---  ---  ---  --- 









   







 -  ------  ----

 ---  ---   

Â&#x2014; 40 Â&#x2014;





    â&#x20AC;&#x201C;   ---  ---    --- â&#x20AC;&#x201C; ---  ---         --------------------------------------------------------------------------  ---

    ---  --- â&#x20AC;&#x201C; --- + --     



  -  ---   ---  ---  ---  ---  --------------







   

  ---  --- 



 ------  -------------------  ---   ---  ---  ---   



   

 ---  ---  ---  

















    â&#x20AC;&#x201C;  +  -  --------  --------  ----------------------------  ------  - ---  ---  ---  ---  . ------







    ---  ---- -----------------  / ---  ----













0  ---

 

     --- + --- â&#x20AC;&#x201C; ---     ---------------------------------------------------------      ---   â&#x20AC;&#x201C; ---  ------  --    

















    ---  --------------- 

     -  -------------------  ------  ---   ---  ----

  







-  ---  --- 





  

---------  ---  ---------  ------   ---    

 

    ------  ----------------  ------  ---   ---       

 -  ---   -----

    -  -------------------    -----

 -    ---  ----



-   ------  ---   -----





 

 ------   ------  -----------------  ---  ---  





   +â&#x20AC;&#x201C;  -  --------  --------  ---------------------  ------   -------

    ------  ------  ----------------------   ---  ---  



     



 

-     ---   ---------------



 



   -  ---  ------  ------  -------------------  ---  ---  ----     







+

-  --------  ------------  ------   --------  -------

  -    ---  -------------------------





      ------  ------  ----------------  ---  ---  . ---  ---  





  

  -  /  ---   ---  --------------





Â&#x2014; 41 Â&#x2014;




   ---  ---  ---   ---  ---

  

-    ---   --------------------









                                                                       



                                               ---  ---  ---  --- 









   







 -  ------  ----

 ---  ---   

Â&#x2014; 40 Â&#x2014;





    â&#x20AC;&#x201C;   ---  ---    --- â&#x20AC;&#x201C; ---  ---         --------------------------------------------------------------------------  ---

    ---  --- â&#x20AC;&#x201C; --- + --     



  -  ---   ---  ---  ---  ---  --------------







   

  ---  --- 



 ------  -------------------  ---   ---  ---  ---   



   

 ---  ---  ---  

















    â&#x20AC;&#x201C;  +  -  --------  --------  ----------------------------  ------  - ---  ---  ---  ---  . ------







    ---  ---- -----------------  / ---  ----













0  ---

 

     --- + --- â&#x20AC;&#x201C; ---     ---------------------------------------------------------      ---   â&#x20AC;&#x201C; ---  ------  --    

















    ---  --------------- 

     -  -------------------  ------  ---   ---  ----

  







-  ---  --- 





  

---------  ---  ---------  ------   ---    

 

    ------  ----------------  ------  ---   ---       

 -  ---   -----

    -  -------------------    -----

 -    ---  ----



-   ------  ---   -----





 

 ------   ------  -----------------  ---  ---  





   +â&#x20AC;&#x201C;  -  --------  --------  ---------------------  ------   -------

    ------  ------  ----------------------   ---  ---  



     



 

-     ---   ---------------



 



   -  ---  ------  ------  -------------------  ---  ---  ----     







+

-  --------  ------------  ------   --------  -------

  -    ---  -------------------------





      ------  ------  ----------------  ---  ---  . ---  ---  





  

  -  /  ---   ---  --------------





Â&#x2014; 41 Â&#x2014;




 + -  ------------  ---  --- ,' ---   ---  ------

  



    --- ,' ---  



   ,-#-9' 







+   -   --------    ---------------    ------    ------   , -#-<   ------





    ,-#-9' 

    ------  ------  ---------------   ---    ,-#-9<       

'

 H %,, #%6 2.6 %      #6$ %                H% 1 -. -#-9'.6 % : # %,   *%  ':-.   %$ %,#'   )%(,%2.6 %%-9''.69, %(-!#'#%66 %#'  â&#x20AC;&#x201C; --        -  ---    ---   ---    ---   -------------  ---   ---------------            â&#x20AC;&#x201C; --- â&#x20AC;&#x201C;  



+   + -  -----------  ------   ----------------------- ----------  â&#x20AC;&#x201C;  â&#x20AC;&#x201C;  â&#x20AC;&#x201C; 

         ---            

             ---   ---      

    â&#x20AC;&#x201C;   + --â&#x20AC;&#x201C; + --â&#x20AC;&#x201C;  --    ---  ----------------------------  -----------------  ----------  ---------    â&#x20AC;&#x201C; â&#x20AC;&#x201C;â&#x20AC;&#x201C; â&#x20AC;&#x201C;  â&#x20AC;&#x201C;   --  â&#x20AC;&#x201C;    â&#x20AC;&#x201C;  

Â&#x2014; 42 Â&#x2014;

)      ---

) )   ),%( #$ %' %  F"        

     )7(#' % ------ ),%(#$%' % F"   



------  % )#'   

 

+%(%9'$#5,#',, @

+  F"#$#% #' -----------------, + ,

+%(%9'$#', ,@ F"#$

+ - #% #' ----------------, â&#x20AC;&#x201C; ,

a

 â&#x20AC;&#x201C;    â&#x20AC;&#x201C;     + -  ------------------------------   -------------  ----------------------------------- -----------------------

 )   

    %        %    %   %> > 

 +    +  -  -----------  ------   --------------- -----------------------  â&#x20AC;&#x201C;   â&#x20AC;&#x201C;    â&#x20AC;&#x201C; 



 

 -   ---- 

- 9' ----

 â&#x20AC;&#x201C;   

  -  ---  --- ,' ---      ----

â&#x20AC;&#x201C;

   -  ---------    ---   ---   -------------

- ---- -  -------,'   ----   

+ -------------  

      

x



b







 +   

   " 2. %

Â&#x2014; 43 Â&#x2014;




 + -  ------------  ---  --- ,' ---   ---  ------

  



    --- ,' ---  



   ,-#-9' 







+   -   --------    ---------------    ------    ------   , -#-<   ------





    ,-#-9' 

    ------  ------  ---------------   ---    ,-#-9<       

'

 H %,, #%6 2.6 %      #6$ %                H% 1 -. -#-9'.6 % : # %,   *%  ':-.   %$ %,#'   )%(,%2.6 %%-9''.69, %(-!#'#%66 %#'  â&#x20AC;&#x201C; --        -  ---    ---   ---    ---   -------------  ---   ---------------            â&#x20AC;&#x201C; --- â&#x20AC;&#x201C;  



+   + -  -----------  ------   ----------------------- ----------  â&#x20AC;&#x201C;  â&#x20AC;&#x201C;  â&#x20AC;&#x201C; 

         ---            

             ---   ---      

    â&#x20AC;&#x201C;   + --â&#x20AC;&#x201C; + --â&#x20AC;&#x201C;  --    ---  ----------------------------  -----------------  ----------  ---------    â&#x20AC;&#x201C; â&#x20AC;&#x201C;â&#x20AC;&#x201C; â&#x20AC;&#x201C;  â&#x20AC;&#x201C;   --  â&#x20AC;&#x201C;    â&#x20AC;&#x201C;  

Â&#x2014; 42 Â&#x2014;

)      ---

) )   ),%( #$ %' %  F"        

     )7(#' % ------ ),%(#$%' % F"   



------  % )#'   

 

+%(%9'$#5,#',, @

+  F"#$#% #' -----------------, + ,

+%(%9'$#', ,@ F"#$

+ - #% #' ----------------, â&#x20AC;&#x201C; ,

a

 â&#x20AC;&#x201C;    â&#x20AC;&#x201C;     + -  ------------------------------   -------------  ----------------------------------- -----------------------

 )   

    %        %    %   %> > 

 +    +  -  -----------  ------   --------------- -----------------------  â&#x20AC;&#x201C;   â&#x20AC;&#x201C;    â&#x20AC;&#x201C; 



 

 -   ---- 

- 9' ----

 â&#x20AC;&#x201C;   

  -  ---  --- ,' ---      ----

â&#x20AC;&#x201C;

   -  ---------    ---   ---   -------------

- ---- -  -------,'   ----   

+ -------------  

      

x



b







 +   

   " 2. %

Â&#x2014; 43 Â&#x2014;


 (      (       (               >  -1,   >     -----------        ---              ---   

  >  -1,  --- >  ---

                  =    -1,  =   ---  ---  



 --- >  --- -1,  --- >  ---    

 )             -1,   

 -  )            =-1,   =

 -  )               = -1,   =

 -   )      > -1, > - )      -1,  - )      =  = -  (4  ''(4   (4 ''(4  (4 ''(4  

- (4  ''(4    ----

(4  ''(4   --- (4 ''(4  

Â&#x2014; 44 Â&#x2014;

  (4#'   '(4#'  '(4#' (4#' &!'%(9,(4#' +,' '(4#'   0#'     0#'    0'#'   0#'     0#'     0'#'   



   >>

 

 

>  >

 >>  > > >> >> H'

?#'9.(>>

 ?#''---,  MMMM MMMMMMMM MMMM H'  ?9.(   ?'---, MM>MM '>  N'-%>=>'!#%< ",(" %(4 + ------------- >  > 

 *%9!9(%$:5 5-9,O

[ â&#x20AC;&#x201C;3

0

) 4

Â&#x2014; 45 Â&#x2014;

x


 (      (       (               >  -1,   >     -----------        ---              ---   

  >  -1,  --- >  ---

                  =    -1,  =   ---  ---  



 --- >  --- -1,  --- >  ---    

 )             -1,   

 -  )            =-1,   =

 -  )               = -1,   =

 -   )      > -1, > - )      -1,  - )      =  = -  (4  ''(4   (4 ''(4  (4 ''(4  

- (4  ''(4    ----

(4  ''(4   --- (4 ''(4  

Â&#x2014; 44 Â&#x2014;

  (4#'   '(4#'  '(4#' (4#' &!'%(9,(4#' +,' '(4#'   0#'     0#'    0'#'   0#'     0#'     0'#'   



   >>

 

 

>  >

 >>  > > >> >> H'

?#'9.(>>

 ?#''---,  MMMM MMMMMMMM MMMM H'  ?9.(   ?'---, MM>MM '>  N'-%>=>'!#%< ",(" %(4 + ------------- >  > 

 *%9!9(%$:5 5-9,O

[ â&#x20AC;&#x201C;3

0

) 4

Â&#x2014; 45 Â&#x2014;

x


Ê ïàðàãðàôó 2                                                                   N

?

 M MM MMMM MM M M  MM  MMMM  MM  M M MM MMM MM  



 ?- >#'%#'#' N = N-%(,MMMM ?-#$ %(#'MM-#$MM  #!9'4(-           " -# %          " # %

                       

  

                                                                                   

       

                  (   (  (    )    )                                            

                           

                               

 

 ),%( -# %    #  )!#' 6 ,    '!'95"#' %< #('1-!#''

— 46 —

— 47 —

 ),%(  "  


Ê ïàðàãðàôó 2                                                                   N

?

 M MM MMMM MM M M  MM  MMMM  MM  M M MM MMM MM  



 ?- >#'%#'#' N = N-%(,MMMM ?-#$ %(#'MM-#$MM  #!9'4(-           " -# %          " # %

                       

  

                                                                                   

       

                  (   (  (    )    )                                            

                           

                               

 

 ),%( -# %    #  )!#' 6 ,    '!'95"#' %< #('1-!#''

— 46 —

— 47 —

 ),%(  "  


Ê ïàðàãðàôó 3                 &#'%##' 0'(,#''$             &#'%#'#' 0''(,#''$               &#'%##' 0'(,#''$             &#'%#'#' 0''(,#''$     8%    0''(,#''$ 8%       0'(,#''$ 8%    0'(,#''$ 8%        0''(,#''$ 8%       0''(,#''$    8%         0'(,#''$ 8%      0''(,#''$ 8%     0''(,#''$ 8%        0'(,#''$ 8%      0''(,#''$                 ;#''''5

— 48 —

                 ;#'''        ;#'''        ;#''''5  D,( %'9.(2('. M M=         MM MM  ?-  ?-  ?-   ) :    ,#''  '%#''.5 '(

  ),#'''5'  K%' ''"'5,1",#''$'9.( '-  ),%(  0'(,#''$ F"' ' )' ,#'''(#'.5 ),%(  0'(,#''$ F"'' )',#'''(#'.5 ),%(   0'(,#''$ F"' ' ---

)' --- ,#'''(#'.5   

   

        1                                                               

— 49 —


Ê ïàðàãðàôó 3                 &#'%##' 0'(,#''$             &#'%#'#' 0''(,#''$               &#'%##' 0'(,#''$             &#'%#'#' 0''(,#''$     8%    0''(,#''$ 8%       0'(,#''$ 8%    0'(,#''$ 8%        0''(,#''$ 8%       0''(,#''$    8%         0'(,#''$ 8%      0''(,#''$ 8%     0''(,#''$ 8%        0'(,#''$ 8%      0''(,#''$                 ;#''''5

— 48 —

                 ;#'''        ;#'''        ;#''''5  D,( %'9.(2('. M M=         MM MM  ?-  ?-  ?-   ) :    ,#''  '%#''.5 '(

  ),#'''5'  K%' ''"'5,1",#''$'9.( '-  ),%(  0'(,#''$ F"' ' )' ,#'''(#'.5 ),%(  0'(,#''$ F"'' )',#'''(#'.5 ),%(   0'(,#''$ F"' ' ---

)' --- ,#'''(#'.5   

   

        1                                                               

— 49 —


'!.6#' ?''%$-1,'< ',#'''2.6'5

                 )!#''%(6 %#'',:%6$. '!%'95#'',:                H 6 %, $6 # 2'  8%  =   #$ %(9"!,#''5-9('-#$#< '  #'%#'#!9'                       

                                         G'5'                           G'5'          

 )  %,''.6#.9'5#'                                            N-,% '5%$2   '( ''",#''$ F"  092 % )< ,    %.#%$ ' # 2.6 '9$

Â&#x2014; 50 Â&#x2014;

 

  , ;#%6< #'" ,,   P'$ #%"'" %< %#,#''                   'I ,  #   / ),%( #5  5 !"#  5 " -#.5  5!"#  5 H%"'!"#<      5 -,%#:%%#$

 5           5   -#.5  5 %  5 #5 0  5 

K.

+

3, %



 

33, %





P'$ '3, %,%#,# !(4%< %#,#''

       

            ' -# , %   ,% %'. ' #<  0,%  

K.

+

D4

 

 

Q'5

R



;Q'$%'# !(4 +%#,#''                     ,D4 ,Q'$ 0

Â&#x2014; 51 Â&#x2014;


'!.6#' ?''%$-1,'< ',#'''2.6'5

                 )!#''%(6 %#'',:%6$. '!%'95#'',:                H 6 %, $6 # 2'  8%  =   #$ %(9"!,#''5-9('-#$#< '  #'%#'#!9'                       

                                         G'5'                           G'5'          

 )  %,''.6#.9'5#'                                            N-,% '5%$2   '( ''",#''$ F"  092 % )< ,    %.#%$ ' # 2.6 '9$

Â&#x2014; 50 Â&#x2014;

 

  , ;#%6< #'" ,,   P'$ #%"'" %< %#,#''                   'I ,  #   / ),%( #5  5 !"#  5 " -#.5  5!"#  5 H%"'!"#<      5 -,%#:%%#$

 5           5   -#.5  5 %  5 #5 0  5 

K.

+

3, %



 

33, %





P'$ '3, %,%#,# !(4%< %#,#''

       

            ' -# , %   ,% %'. ' #<  0,%  

K.

+

D4

 

 

Q'5

R



;Q'$%'# !(4 +%#,#''                     ,D4 ,Q'$ 0

Â&#x2014; 51 Â&#x2014;


 ),%(, '9'.- ('",! '5 F" %%'2#'" F' #'( ' %'2'(4  -  %'2!<  '  '5 (4        '5   9 %%'2#'   F"                , '9'.- ('",! '5  ),%(%#.-''$!! '5"#%(!!%%< ! !5 F#'(#.-'$' !5 (4   !5!!#.-''(4 '  '$    !     '5 % #%6 !5 9' #.!('     F"                 S#.-''$!! '5  ),%( !,' %  " -% #.-''$ ,!'< '.65%#5-,   #'!,''< , %,-1,                    !,' %

à ë à â à II ÔÓÍÊÖÈÈ

§ 4. Ôóíêöèè è èõ ãðàôèêè 10. ×òî òàêîå ôóíêöèÿ   

   

     

        +& &  +  +  &  +  +    ?-         +,& P' '$& %(-'$ I,'2  T%( -< '$ 0 %#5-9,  & ' +  &  ' ' +                      T '  T'   (2  (( '-' %'2 % H''%,  (2 2(        T%(-'$0'9%#',('.6 %  T%(!' '5 0 % 

— 52 —

— 53 —


 ),%(, '9'.- ('",! '5 F" %%'2#'" F' #'( ' %'2'(4  -  %'2!<  '  '5 (4        '5   9 %%'2#'   F"                , '9'.- ('",! '5  ),%(%#.-''$!! '5"#%(!!%%< ! !5 F#'(#.-'$' !5 (4   !5!!#.-''(4 '  '$    !     '5 % #%6 !5 9' #.!('     F"                 S#.-''$!! '5  ),%( !,' %  " -% #.-''$ ,!'< '.65%#5-,   #'!,''< , %,-1,                    !,' %

à ë à â à II ÔÓÍÊÖÈÈ

§ 4. Ôóíêöèè è èõ ãðàôèêè 10. ×òî òàêîå ôóíêöèÿ   

   

     

        +& &  +  +  &  +  +    ?-         +,& P' '$& %(-'$ I,'2  T%( -< '$ 0 %#5-9,  & ' +  &  ' ' +                      T '  T'   (2  (( '-' %'2 % H''%,  (2 2(        T%(-'$0'9%#',('.6 %  T%(!' '5 0 % 

— 52 —

— 53 —


  ",'!' '$",'%,9 %    !' '$I,'20 %   )  -   1- . #.-,7' #    1< -0#



 ),%( #. %' -#', !   H 3 !#, #(%$    #.#'%'   #< . L!33 !#,#.(%$  #.#'%< '%$    F#.%'-#',%%#,#''                 #.%'-#', ! 





B

0

1













































 





 





    T%(-'$%%!#%6 %  -  T%( -'$ %% ! #%6 %    ---------- â&#x20AC;&#x201C;

    -----------  T%( -'$ %% ! #%6 % +



D

â&#x20AC;&#x201C; ---------------- T%(-'$%%!#%6 %   

x



A

                       

11. Ã&#x201A;û÷èñëåíèå çíà ÷åíèé ôóíêöèè ïî ôîðìóëå



    

      

             

        

         





















 ------   

 ------  â&#x20AC;&#x201C;

 ------  â&#x20AC;&#x201C;

 ------ 

 ------  









  --









  

 ------   â&#x20AC;&#x201C;

  





   

                                 

C 1



                    

# $ 

y

 ---   ---  ---  ---  



  ---  

   ---   

  



  -    ---  --------------------







-  -    ---   ------------

 ------  



Â&#x2014; 54 Â&#x2014;





  ---  --------- 



Â&#x2014; 55 Â&#x2014;


  ",'!' '$",'%,9 %    !' '$I,'20 %   )  -   1- . #.-,7' #    1< -0#



 ),%( #. %' -#', !   H 3 !#, #(%$    #.#'%'   #< . L!33 !#,#.(%$  #.#'%< '%$    F#.%'-#',%%#,#''                 #.%'-#', ! 





B

0

1













































 





 





    T%(-'$%%!#%6 %  -  T%( -'$ %% ! #%6 %    ---------- â&#x20AC;&#x201C;

    -----------  T%( -'$ %% ! #%6 % +



D

â&#x20AC;&#x201C; ---------------- T%(-'$%%!#%6 %   

x



A

                       

11. Ã&#x201A;û÷èñëåíèå çíà ÷åíèé ôóíêöèè ïî ôîðìóëå



    

      

             

        

         





















 ------   

 ------  â&#x20AC;&#x201C;

 ------  â&#x20AC;&#x201C;

 ------ 

 ------  









  --









  

 ------   â&#x20AC;&#x201C;

  





   

                                 

C 1



                    

# $ 

y

 ---   ---  ---  ---  



  ---  

   ---   

  



  -    ---  --------------------







-  -    ---   ------------

 ------  



Â&#x2014; 54 Â&#x2014;





  ---  --------- 



Â&#x2014; 55 Â&#x2014;


         3                 %  



   "

0



 +, , @ +   + , , @ 

    T%(-'$15I,'20',('. %  #: ('  / ),%( 4%%%' %  '" " %%< %' %      '"  H%" %            '"  - ,%#: #'   +%# ,#''         '"  %%%'% '"

B

1

----------- %     

 + & +     + &  &  &  & &    

5

y

M 1

x

A

12. Ãðàôèê ôóíêöèè 































 



   



 



 



 

 

      ! "#                  

y 10

0

1

x





4

y









   

N

1 0

1

K

x





y 8

  

1

M

–1 0

— 56 —

— 57 —

1

5

x


         3                 %  



   "

0



 +, , @ +   + , , @ 

    T%(-'$15I,'20',('. %  #: ('  / ),%( 4%%%' %  '" " %%< %' %      '"  H%" %            '"  - ,%#: #'   +%# ,#''         '"  %%%'% '"

B

1

----------- %     

 + & +     + &  &  &  & &    

5

y

M 1

x

A

12. Ãðàôèê ôóíêöèè 































 



   



 



 



 

 

      ! "#                  

y 10

0

1

x





4

y









   

N

1 0

1

K

x





y 8

  

1

M

–1 0

— 56 —

— 57 —

1

5

x








 ---  

 --- 

 ---  





 ---  

 --- 

 ---  

     

     

 

 

   



 

y

 

6

   

0 1

6

x

 

 



 

















y N

 

  

  

1 0

1

x P

 %       &#'%##' F % -'9"I,I,'2 "      &#'%##' F "-'9"I,I,'2 #      &#'%#'#' F #'-'9"I, I,'2 ?- $ -'9"I,I,'2 ) '-'9"I,I,'2  %     &#'%##' F %-'9"I, "    &#'%##' F "-'9"I, #        &#'%#'#' F #'-'9"I, 

1

Â&#x2014; 58 Â&#x2014;

x B

M

y

0

   

      

  3  3  

                    









1 1

A





    

   





  





    

C



 

1

   







 

y

0

)9('.!' '$I,'2'--     T2('.!' '$I,'2'--       

  

1

x























Â&#x2014; 59 Â&#x2014;








 ---  

 --- 

 ---  





 ---  

 --- 

 ---  

     

     

 

 

   



 

y

 

6

   

0 1

6

x

 

 



 

















y N

 

  

  

1 0

1

x P

 %       &#'%##' F % -'9"I,I,'2 "      &#'%##' F "-'9"I,I,'2 #      &#'%#'#' F #'-'9"I, I,'2 ?- $ -'9"I,I,'2 ) '-'9"I,I,'2  %     &#'%##' F %-'9"I, "    &#'%##' F "-'9"I, #        &#'%#'#' F #'-'9"I, 

1

Â&#x2014; 58 Â&#x2014;

x B

M

y

0

   

      

  3  3  

                    









1 1

A





    

   





  





    

C



 

1

   







 

y

0

)9('.!' '$I,'2'--     T2('.!' '$I,'2'--       

  

1

x























Â&#x2014; 59 Â&#x2014;


)"I,

           

                

y

1   

10

)I,

-                   -----



    ------ 





            

4,7

1 0 1 2,5   "  "  "  

x

m, êã 5

  ---  ---  ---  --- =

4













                ------  --- $ --- % &'(! ---  ---  ---  --- % '       

2 1

 *!' 0 °C + 100 *!  ' 0 + *! ' 0+ 80 *!' 0 60 +  + 0 ! 40 ',.  + 0 ! 20 ',.

+ 0 ! 0 ',.





â&#x20AC;&#x201C;+   -  --------  --------  --------  ---------------------   ---  ---  ---  ---  -----

3

0

 ),%("#.64'. ",!#.6 4, )%<  -, '$ "#.6 4' 6 %      4'  ",!#.6%  4' P'$ "#.6< 4'%'(4%%#,#''                 U"#.64'. ",!#.6 0   ##-.#%" #4'

1

2

3

4

5

6 V, ë

     >    $  $   $ =  ?#'%#     >  '#'

§ 5. Ã&#x2039;èíåéíà ÿ ôóíêöèÿ 13. Ã&#x2039;èíåéíàÿ ôóíêöèÿ è åå ãðàôèê    V!#%%($#$%$'5'5I,'25

2

4

6

8

10 12 ìèí

 ?%,6%I(0  ?%I(0   )"0 ?%,6%I( 0' @ H9( 0 @ )" 0 @

Â&#x2014; 60 Â&#x2014;

 6    6   6       U'5'5$#$%$!#%%(6        V!#%%($#$%$'5'5I,'25  N  

   ---  ? ?    

Â&#x2014; 61 Â&#x2014;


)"I,

           

                

y

1   

10

)I,

-                   -----



    ------ 





            

4,7

1 0 1 2,5   "  "  "  

x

m, êã 5

  ---  ---  ---  --- =

4













                ------  --- $ --- % &'(! ---  ---  ---  --- % '       

2 1

 *!' 0 °C + 100 *!  ' 0 + *! ' 0+ 80 *!' 0 60 +  + 0 ! 40 ',.  + 0 ! 20 ',.

+ 0 ! 0 ',.





â&#x20AC;&#x201C;+   -  --------  --------  --------  ---------------------   ---  ---  ---  ---  -----

3

0

 ),%("#.64'. ",!#.6 4, )%<  -, '$ "#.6 4' 6 %      4'  ",!#.6%  4' P'$ "#.6< 4'%'(4%%#,#''                 U"#.64'. ",!#.6 0   ##-.#%" #4'

1

2

3

4

5

6 V, ë

     >    $  $   $ =  ?#'%#     >  '#'

§ 5. Ã&#x2039;èíåéíà ÿ ôóíêöèÿ 13. Ã&#x2039;èíåéíàÿ ôóíêöèÿ è åå ãðàôèê    V!#%%($#$%$'5'5I,'25

2

4

6

8

10 12 ìèí

 ?%,6%I(0  ?%I(0   )"0 ?%,6%I( 0' @ H9( 0 @ )" 0 @

Â&#x2014; 60 Â&#x2014;

 6    6   6       U'5'5$#$%$!#%%(6        V!#%%($#$%$'5'5I,'25  N  

   ---  ? ?    

Â&#x2014; 61 Â&#x2014;


        

    

                            

  --- 



y

1 1 0

1

  

 

0 1

x

 

y

0 1

 

x

 

 

 

y

1

1

1 0 1

x

0 1

Â&#x2014; 62 Â&#x2014;

x

0 1

x

  

  

y 1 1 x

1 0 1



y

0 1

x

  

y

y

0 1

x

  

  

  

 

1

1

   

  

 

y

y

y

          

          

    >       1                                  

   

  

   

 

x

Â&#x2014; 63 Â&#x2014;

0 1

x


        

    

                            

  --- 



y

1 1 0

1

  

 

0 1

x

 

y

0 1

 

x

 

 

 

y

1

1

1 0 1

x

0 1

Â&#x2014; 62 Â&#x2014;

x

0 1

x

  

  

y 1 1 x

1 0 1



y

0 1

x

  

y

y

0 1

x

  

  

  

 

1

1

   

  

 

y

y

y

          

          

    >       1                                  

   

  

   

 

x

Â&#x2014; 63 Â&#x2014;

0 1

x


  



   

      

  

y

    





 

1 0 1

x



y,°C 100

80 *! '   + *! 60 ' + N +#'< 40 "%( !  ' 20 0

  

 

 





1 0 1

  

 

70

 

   

 

     

20 30

40 50

60 x, ìèí

y

 

  

      

10

x

y

60

             WI-%%( # 

50

3 3 3







 ---  

40

  --- 

30

WI-%%( #  



20 10 0 1 â&#x20AC;&#x201C;10 â&#x20AC;&#x201C;20

Â&#x2014; 64 Â&#x2014;

    

 3                

                

              

            

5

x





 ---   

 

 %    WI-6 !'',: , "          WI-6 !'',: , #        WI'-6 !'',: , $        WI-6 !'',: ,

Â&#x2014; 65 Â&#x2014;


  



   

      

  

y

    





 

1 0 1

x



y,°C 100

80 *! '   + *! 60 ' + N +#'< 40 "%( !  ' 20 0

  

 

 





1 0 1

  

 

70

 

   

 

     

20 30

40 50

60 x, ìèí

y

 

  

      

10

x

y

60

             WI-%%( # 

50

3 3 3







 ---  

40

  --- 

30

WI-%%( #  



20 10 0 1 â&#x20AC;&#x201C;10 â&#x20AC;&#x201C;20

Â&#x2014; 64 Â&#x2014;

    

 3                

                

              

            

5

x





 ---   

 

 %    WI-6 !'',: , "          WI-6 !'',: , #        WI'-6 !'',: , $        WI-6 !'',: ,

Â&#x2014; 65 Â&#x2014;


 # 2

y = –1 y = –5

N$#$%$   --- 

 N ?

y = 3,2 y=0

N$#$%$

1 0 1

x

y = 1,6 y = –1,9

1 0 1

   

x

y = –2

 

   

                                       >  > N(,-#('5-        N(,'-#('5- 

 ---   ---  ---  ---   ---





 ---     ---  ---   ---   





  ---  ---  ---   --- 







  ---  --- 

 

 ---  

 --- 

 ---  --- 

 ---  ---  ---  



 ---  

   ---   





   ---    

  

 

y

 

1

 

0

x

–x

— 67 —

1 =

 

y

 



x





,5 –1

 

 





 --- 

  

 



     

— 66 —

?

y=

 / ),%(-#$"!"# 5"#$ !"# 5($0      H%"!"#   5  -,%#:#' $ +%#,#''                  

       -#$"!"# 5#$0 5($0 5

x

y

 + &

y= 3x

y=7

y=6

14. Ïðÿìàÿ ïðîïîðöèîíàëüíîñòü

=

y

 WI ''.6 I,'< 25 0 -$. -< ('.% 

y

 WI ''.6 I,'< 25 0 -$. -< ('.%


 # 2

y = –1 y = –5

N$#$%$   --- 

 N ?

y = 3,2 y=0

N$#$%$

1 0 1

x

y = 1,6 y = –1,9

1 0 1

   

x

y = –2

 

   

                                       >  > N(,-#('5-        N(,'-#('5- 

 ---   ---  ---  ---   ---





 ---     ---  ---   ---   





  ---  ---  ---   --- 







  ---  --- 

 

 ---  

 --- 

 ---  --- 

 ---  ---  ---  



 ---  

   ---   





   ---    

  

 

y

 

1

 

0

x

–x

— 67 —

1 =

 

y

 



x





,5 –1

 

 





 --- 

  

 



     

— 66 —

?

y=

 / ),%(-#$"!"# 5"#$ !"# 5($0      H%"!"#   5  -,%#:#' $ +%#,#''                  

       -#$"!"# 5#$0 5($0 5

x

y

 + &

y= 3x

y=7

y=6

14. Ïðÿìàÿ ïðîïîðöèîíàëüíîñòü

=

y

 WI ''.6 I,'< 25 0 -$. -< ('.% 

y

 WI ''.6 I,'< 25 0 -$. -< ('.%


   





1

 

0 y= 2,5x

 

 



x

y= â&#x20AC;&#x201C;0 ,5   

x

1 0

 























 





y

10

5

0 1

1

x

 % 

   ---   

1 0

 -  

1

x

% 

 

 





)'9 " 

  

?-'9 " 

  

   ---   --- 

 





---  

?-'9

Â&#x2014; 68 Â&#x2014;

x

 )46.#-, #%-%  )46- #%-% +%(-46 @ #%-% @  H%-%-6!  #!(< 4 -4-46  %      XY-'9"I, "         )'9"I, #         )'9"I, $         )'9"I,

y

   

5

 )*

 

  

  







P#%%(    -< 9''!I,  

 -  -    -  P' ' -  %,7%#,    



y

 

  





1

4,5x y=â&#x20AC;&#x201C;

 



y

)'9

Â&#x2014; 69 Â&#x2014;




   





1

 

0 y= 2,5x

 

 



x

y= â&#x20AC;&#x201C;0 ,5   

x

1 0

 























 





y

10

5

0 1

1

x

 % 

   ---   

1 0

 -  

1

x

% 

 

 





)'9 " 

  

?-'9 " 

  

   ---   --- 

 





---  

?-'9

Â&#x2014; 68 Â&#x2014;

x

 )46.#-, #%-%  )46- #%-% +%(-46 @ #%-% @  H%-%-6!  #!(< 4 -4-46  %      XY-'9"I, "         )'9"I, #         )'9"I, $         )'9"I,

y

   

5

 )*

 

  

  







P#%%(    -< 9''!I,  

 -  -    -  P' ' -  %,7%#,    



y

 

  





1

4,5x y=â&#x20AC;&#x201C;

 



y

)'9

Â&#x2014; 69 Â&#x2014;




#

 

#

 

 ---  

 

 ---  

  

?-'9

$   ---  --- 

$   ---  --- 







 ---   --- 





0



 ---    ---   ---  ---  ---

   ---   ---  --- $ ---  ---

?-'9 )

 

?-'9 )

 

 --- 



















y

1 x

0 1

x

>

0

1

1 1

x

0 1

x

>

=

--- =  

 --- > 

15. Ã&#x201A;çà èìíîå ðàñïîëîæåíèå ãðàôèêîâ ëèíåéíûõ ôóíêöèé  WI-('. WI-%:%$ WI-%:%$

Â&#x2014; 70 Â&#x2014;

x

  

   

          

                 

 =

y

y

1

             

  

 

0

x

33 =       ---    333 >    ---  ---  ---   3Z >     ---   

y

1 0 1

1

 3 =     ---   



 

 

1





)'9

)'9

>

y

1

 ---   ---



  

y



?-'9

=

WI-%:%$ WI-('. WI-%:%$

Â&#x2014; 71 Â&#x2014;


#

 

#

 

 ---  

 

 ---  

  

?-'9

$   ---  --- 

$   ---  --- 







 ---   --- 





0



 ---    ---   ---  ---  ---

   ---   ---  --- $ ---  ---

?-'9 )

 

?-'9 )

 

 --- 



















y

1 x

0 1

x

>

0

1

1 1

x

0 1

x

>

=

--- =  

 --- > 

15. Ã&#x201A;çà èìíîå ðàñïîëîæåíèå ãðàôèêîâ ëèíåéíûõ ôóíêöèé  WI-('. WI-%:%$ WI-%:%$

Â&#x2014; 70 Â&#x2014;

x

  

   

          

                 

 =

y

y

1

             

  

 

0

x

33 =       ---    333 >    ---  ---  ---   3Z >     ---   

y

1 0 1

1

 3 =     ---   



 

 

1





)'9

)'9

>

y

1

 ---   ---



  

y



?-'9

=

WI-%:%$ WI-('. WI-%:%$

Â&#x2014; 71 Â&#x2014;


     )%:%$

               

â&#x20AC;&#x201C;x +

y = â&#x20AC;&#x201C;x â&#x20AC;&#x201C; 1,5 y y = 0,5x + 2,5 y = 2,5

   









6

  

   

=

 

x

3

   

    

 

1

â&#x20AC;&#x201C;

Â&#x2014; 72 Â&#x2014;

 

0

â&#x20AC;&#x201C;x

       )%:%$         

              )%:%$                    



y

 

1 =

1 0 1

x

y = x + 2,5 y = â&#x20AC;&#x201C;x + 2,5

               

 

 

  



y



y = 3x

1  



 

Â&#x2014; 73 Â&#x2014;

0

1

y= 3x â&#x20AC;&#x201C; 4

    3                      0'. -% '$                             0'. -% '$                     0'. -% '$                       0'. -% '$                        0'. -% '$              0'. -% '$

â&#x20AC;&#x201C;x



    

y

   

y =

 

 

 

            ---

?-%:%$

y

              

     --- 

y= 3x + 1,2

 WI-('.,I,'25            WI-%:%$,I,'25         

x


     )%:%$

               

â&#x20AC;&#x201C;x +

y = â&#x20AC;&#x201C;x â&#x20AC;&#x201C; 1,5 y y = 0,5x + 2,5 y = 2,5

   









6

  

   

=

 

x

3

   

    

 

1

â&#x20AC;&#x201C;

Â&#x2014; 72 Â&#x2014;

 

0

â&#x20AC;&#x201C;x

       )%:%$         

              )%:%$                    



y

 

1 =

1 0 1

x

y = x + 2,5 y = â&#x20AC;&#x201C;x + 2,5

               

 

 

  



y



y = 3x

1  



 

Â&#x2014; 73 Â&#x2014;

0

1

y= 3x â&#x20AC;&#x201C; 4

    3                      0'. -% '$                             0'. -% '$                     0'. -% '$                       0'. -% '$                        0'. -% '$              0'. -% '$

â&#x20AC;&#x201C;x



    

y

   

y =

 

 

 

            ---

?-%:%$

y

              

     --- 

y= 3x + 1,2

 WI-('.,I,'25            WI-%:%$,I,'25         

x


2

 

0 1

x

>

        ------ > =  

 > =

–x –



2

    

    

y

y= 17x + 20

40

y 0x y = –3

50

30 20 10 0 1

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå II Ê ïàðàãðàôó 4  -    ---------

  

50

   ">M M T%(-'$0#%  M M = 

  

  

40

  ------ @  , +--  

30

&

10 x

–20

–20

–30

–30

–40

–40

— 74 —

0x + 8 y = –3

0 1 –10



'0-#.5-# '0#5  0!-#.5 %  0!-%'5   0'-#.   0'#.  

20

–10 y= 17x

33 >

=

 

  

 

WI%-9'#3333''.6 < #$6     WI%-9'#333Z''.6 < #$6 

=

y

–2 ,4x 0 y=

  



1

 ),%(#3'(!#! !'# 33 0  !' H%"!#! 



!' -,%#:#'   

        #3'(!#! !'



 3 =

x

 

y

=



  

y

      

x







 

 





















'!#%$-''$ !#%$             -        -   -     

— 75 —


2

 

0 1

x

>

        ------ > =  

 > =

–x –



2

    

    

y

y= 17x + 20

40

y 0x y = –3

50

30 20 10 0 1

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå II Ê ïàðàãðàôó 4  -    ---------

  

50

   ">M M T%(-'$0#%  M M = 

  

  

40

  ------ @  , +--  

30

&

10 x

–20

–20

–30

–30

–40

–40

— 74 —

0x + 8 y = –3

0 1 –10



'0-#.5-# '0#5  0!-#.5 %  0!-%'5   0'-#.   0'#.  

20

–10 y= 17x

33 >

=

 

  

 

WI%-9'#3333''.6 < #$6     WI%-9'#333Z''.6 < #$6 

=

y

–2 ,4x 0 y=

  



1

 ),%(#3'(!#! !'# 33 0  !' H%"!#! 



!' -,%#:#'   

        #3'(!#! !'



 3 =

x

 

y

=



  

y

      

x







 

 





















'!#%$-''$ !#%$             -        -   -     

— 75 —


































       



    



     











 





 







  +  -  ------- 

 â&#x20AC;&#x201C;---------------------

  +  -  ------- 

 â&#x20AC;&#x201C;-------------------- 

  +  -  -------  

 --------------- 

     





y



         

 H% %  H% % 

-----------------        

      

                       

1 0

1



â&#x20AC;&#x201C;2 0 2

Â&#x2014; 76 Â&#x2014;

12

x

x

1

 --- 

 

1 â&#x20AC;&#x201C;2

5

0

  

x

y

          

y

1

â&#x20AC;&#x201C;2

    

 

     

     



    



 

x

â&#x20AC;&#x201C;14

+

 -----------

   ---  

â&#x20AC;&#x201C;2 1 0 2

 

â&#x20AC;&#x201C;10

               



y

 )    )  > > ) >  =

Â&#x2014; 77 Â&#x2014;


































       



    



     











 





 







  +  -  ------- 

 â&#x20AC;&#x201C;---------------------

  +  -  ------- 

 â&#x20AC;&#x201C;-------------------- 

  +  -  -------  

 --------------- 

     





y



         

 H% %  H% % 

-----------------        

      

                       

1 0

1



â&#x20AC;&#x201C;2 0 2

Â&#x2014; 76 Â&#x2014;

12

x

x

1

 --- 

 

1 â&#x20AC;&#x201C;2

5

0

  

x

y

          

y

1

â&#x20AC;&#x201C;2

    

 

     

     



    



 

x

â&#x20AC;&#x201C;14

+

 -----------

   ---  

â&#x20AC;&#x201C;2 1 0 2

 

â&#x20AC;&#x201C;10

               



y

 )    )  > > ) >  =

Â&#x2014; 77 Â&#x2014;


 8%     %  8%  %  

    

                   ),%(      

  )  !' 'I,'2#'!' ':",' ),%(       

V, ë 25 20 15 10 5 0

 ------   ---    

2

4

6

8





H, ñì

)  --- !' 'I,'2-#-9'!' ':

10 12 14 16



",'   T!   T!.#4  '09      ..#'!  *!   -% #.6 !  .# . ' %< %$'   ?%%$''. !  -% #.6'-,, !  -%#.6'-,< '

 





------  @  +'$$%%(''-,<   

$9













 





















– ----------------       

E#$%$

       E#$%$       ?$#$%$             E#$%$       

   

E#$%$              E#$%$   

 



)   !'    )%(, -   L  

Ê ïàðàãðàôó 5



)   !'    )%(,  -        L  

 +'$$%%('-,,    ---   --- 

     

— 78 —



























)   -       -  )1,   )##-  1,I,,,9%$  '#'  

V'5'$I,'2$

— 79 —


 8%     %  8%  %  

    

                   ),%(      

  )  !' 'I,'2#'!' ':",' ),%(       

V, ë 25 20 15 10 5 0

 ------   ---    

2

4

6

8





H, ñì

)  --- !' 'I,'2-#-9'!' ':

10 12 14 16



",'   T!   T!.#4  '09      ..#'!  *!   -% #.6 !  .# . ' %< %$'   ?%%$''. !  -% #.6'-,, !  -%#.6'-,< '

 





------  @  +'$$%%(''-,<   

$9













 





















– ----------------       

E#$%$

       E#$%$       ?$#$%$             E#$%$       

   

E#$%$              E#$%$   

 



)   !'    )%(, -   L  

Ê ïàðàãðàôó 5



)   !'    )%(,  -        L  

 +'$$%%('-,,    ---   --- 

     

— 78 —



























)   -       -  )1,   )##-  1,I,,,9%$  '#'  

V'5'$I,'2$

— 79 —


  

  

y

1   

   x 0 1

    

  

 

  G'.   -% '$ "I % %$ < '                 -    -   

 

 

 

 



y

500 400 300 200 100

5 4 3 2 1

0

2 3 4

x

 F %-'9"I,%     ---  

  --- 



1

9-'(2. !' '$ 

200 400 0 100 300 x

 

 %           WI-6 ! ,% 4            WI-6 ! ,4

â&#x20AC;&#x201C;1 0 1

x

êì 75

 

60

P #%-%-<  !  '   ?-,(# #%< -%!  '  & [ & [

Â&#x2014; 80 Â&#x2014;

y



 

y

1

6           WI'-6 ! ,6 7                  WI'-6 ! ,7

45 30 15 0

1

2

3

4

5

, @% , @%

   )%    0'. -% '$    )%      0'. -% '$    )%    0'. -% '$

Â&#x2014; 81 Â&#x2014;

÷


  

  

y

1   

   x 0 1

    

  

 

  G'.   -% '$ "I % %$ < '                 -    -   

 

 

 

 



y

500 400 300 200 100

5 4 3 2 1

0

2 3 4

x

 F %-'9"I,%     ---  

  --- 



1

9-'(2. !' '$ 

200 400 0 100 300 x

 

 %           WI-6 ! ,% 4            WI-6 ! ,4

â&#x20AC;&#x201C;1 0 1

x

êì 75

 

60

P #%-%-<  !  '   ?-,(# #%< -%!  '  & [ & [

Â&#x2014; 80 Â&#x2014;

y



 

y

1

6           WI'-6 ! ,6 7                  WI'-6 ! ,7

45 30 15 0

1

2

3

4

5

, @% , @%

   )%    0'. -% '$    )%      0'. -% '$    )%    0'. -% '$

Â&#x2014; 81 Â&#x2014;

÷


                  0'. -% '$         0'. -% '$

  )%    0'. -% '$   ?-%   ?-%  



y

y y =

y= ax x

1 1 0

x

= y         5           F 5-'9"I,  F  -$$ -(' "I, I,'2       I,'2$!%$I,5   )%(,-$$-6 < !%      T' (' 

y

1 0 1

 

  

? '9#',,"('

A(2; 3) 0

1

x

                       0'. -% '$                         0'. -% '$

Â&#x2014; 82 Â&#x2014;

x

y = â&#x20AC;&#x201C;2x + 3

y

1

y = 3x + 2

y = 0,5x â&#x20AC;&#x201C; 2

 

   

ax

0 1

bx

1

bx y=

  

 

Â&#x2014; 83 Â&#x2014;


                  0'. -% '$         0'. -% '$

  )%    0'. -% '$   ?-%   ?-%  



y

y y =

y= ax x

1 1 0

x

= y         5           F 5-'9"I,  F  -$$ -(' "I, I,'2       I,'2$!%$I,5   )%(,-$$-6 < !%      T' (' 

y

1 0 1

 

  

? '9#',,"('

A(2; 3) 0

1

x

                       0'. -% '$                         0'. -% '$

Â&#x2014; 82 Â&#x2014;

x

y = â&#x20AC;&#x201C;2x + 3

y

1

y = 3x + 2

y = 0,5x â&#x20AC;&#x201C; 2

 

   

ax

0 1

bx

1

bx y=

  

 

Â&#x2014; 83 Â&#x2014;


à ë à â à III ÑÒÅÏÅÍÜ Ñ ÍÀÒÓÐÀËÜÍÛÌ ÏÎÊÀÇÀÒÅËÅÌ

§ 6. Ñòåïåíü è åå ñâîéñòâà 16. Îïðåäåëåíèå ñòåïåíè ñ íàòóðàëüíûì ïîêàçàòåëåì            ---  ---  ---  ---   --- 







   !







 !

  ---   --- %'#' 0-!(

       ---    ---   ---   ---   ---   ---         

                            

 -

  ---   ---  ---  ---  ---  -------



 

      

           0%'#' 0-!(       0%'#' 0-!(      0%'#' 0-!(

     0%'#' 0-!( 

— 84 —









 -    ---     ---     ---     ---     ---     ---   -------       

    ---     ---     ---     --- 



 0%'#' 0-!(  



 ---------  ------

   ---    ---   ---  ---  ---  ---        



 



---------  ---    ---     ---     ---     ---     ---   

                          

 -

   ---     ---     ---     ---     ---     ---    ----  

 -    ---     ---     ---     ---     ---     ---    ---   ---- 

   

      

     

           

— 85 —


à ë à â à III ÑÒÅÏÅÍÜ Ñ ÍÀÒÓÐÀËÜÍÛÌ ÏÎÊÀÇÀÒÅËÅÌ

§ 6. Ñòåïåíü è åå ñâîéñòâà 16. Îïðåäåëåíèå ñòåïåíè ñ íàòóðàëüíûì ïîêàçàòåëåì            ---  ---  ---  ---   --- 







   !







 !

  ---   --- %'#' 0-!(

       ---    ---   ---   ---   ---   ---         

                            

 -

  ---   ---  ---  ---  ---  -------



 

      

           0%'#' 0-!(       0%'#' 0-!(      0%'#' 0-!(

     0%'#' 0-!( 

— 84 —









 -    ---     ---     ---     ---     ---     ---   -------       

    ---     ---     ---     --- 



 0%'#' 0-!(  



 ---------  ------

   ---    ---   ---  ---  ---  ---        



 



---------  ---    ---     ---     ---     ---     ---   

                          

 -

   ---     ---     ---     ---     ---     ---    ----  

 -    ---     ---     ---     ---     ---     ---    ---   ---- 

   

      

     

           

— 85 —


                            

 















 











        

-   ------            -------  



 ------  ------   ---     ---        



 

    





    -    ---   ------  ---------   ---     ---   ----       

                      

      

    ------   ---     ---   ---     



   ------  ------   ---     --- 

     

     =          > -1, >            >      =  -1,   >          =   > -1,  =  

  

    

    

    

     

     

    

Â&#x2014; 86 Â&#x2014;

                 

 ------  ------  ---      ---       





   -   ------   ---------   ---     ---    -----------      

      

                

 

 

                           

                                   

   ---    

     

         )  

     ) 

   ) 

   ) 

     )       )    )   

Â&#x2014; 87 Â&#x2014;


                            

 















 











        

-   ------            -------  



 ------  ------   ---     ---        



 

    





    -    ---   ------  ---------   ---     ---   ----       

                      

      

    ------   ---     ---   ---     



   ------  ------   ---     --- 

     

     =          > -1, >            >      =  -1,   >          =   > -1,  =  

  

    

    

    

     

     

    

Â&#x2014; 86 Â&#x2014;

                 

 ------  ------  ---      ---       





   -   ------   ---------   ---     ---    -----------      

      

                

 

 

                           

                                   

   ---    

     

         )  

     ) 

   ) 

   ) 

     )       )    )   

Â&#x2014; 87 Â&#x2014;


 )     )     )    )        )    )         )      )    )      )    )        )     )    )    )   )    )   )   

 )                    )                    

 



  

    - :    '$ %-'( :" % %( % '2('   =  %#('     -:     -:  '$%-'(:" %%( %'2('   =-:1%,'2(< '" %-9('" Q'" '  =-:

Â&#x2014; 88 Â&#x2014;

    G#%,. %    +,## %     G#!'% %    &!'%(## %    G,!'% %     +,,# % 

  ;#''.5#!'% %     ;''$%,## %              

 )   )     )        

 

            

 

                 

         0'. -% '$                            0'. -% '$  WI-('. WI-%:%$

17. Ã&#x201C;ìíîæåíèå è äåëåíèå ñòåïåíåé   

       

   

 

    

    '''

         

  

      

Â&#x2014; 89 Â&#x2014;

            


 )     )     )    )        )    )         )      )    )      )    )        )     )    )    )   )    )   )   

 )                    )                    

 



  

    - :    '$ %-'( :" % %( % '2('   =  %#('     -:     -:  '$%-'(:" %%( %'2('   =-:1%,'2(< '" %-9('" Q'" '  =-:

Â&#x2014; 88 Â&#x2014;

    G#%,. %    +,## %     G#!'% %    &!'%(## %    G,!'% %     +,,# % 

  ;#''.5#!'% %     ;''$%,## %              

 )   )     )        

 

            

 

                 

         0'. -% '$                            0'. -% '$  WI-('. WI-%:%$

17. Ã&#x201C;ìíîæåíèå è äåëåíèå ñòåïåíåé   

       

   

 

    

    '''

         

  

      

Â&#x2014; 89 Â&#x2014;

            


   

    

        

        

    

     

'''''            

                                                                                



'''

  

  

  

   

 

 

â&#x20AC;&#x201C;      -----------------  â&#x20AC;&#x201C;  

   ---    -------------- -    ---    ---   ---  ---     ---     â&#x20AC;&#x201C;  ---     ---------  

------  ------------------    ---     ---          â&#x20AC;&#x201C;   -- 



  -  --------     --------------  



    -  --------    --------------    





    -  -------------    ------------------------    

  

    

   

              

  ------  ---    ---     ---     ---    ---        

Â&#x2014; 90 Â&#x2014;





  ' ''

    

 





 ---------  

  ------  

 -  --------    -----------------



 

   

  

-    ---     ---     ---   ----     

    

             

    

           

       

   -  

        ---     

   -  --- 





 -       - ---  ---  



    -     ---     ---      ----   

Â&#x2014; 91 Â&#x2014;


   

    

        

        

    

     

'''''            

                                                                                



'''

  

  

  

   

 

 

â&#x20AC;&#x201C;      -----------------  â&#x20AC;&#x201C;  

   ---    -------------- -    ---    ---   ---  ---     ---     â&#x20AC;&#x201C;  ---     ---------  

------  ------------------    ---     ---          â&#x20AC;&#x201C;   -- 



  -  --------     --------------  



    -  --------    --------------    





    -  -------------    ------------------------    

  

    

   

              

  ------  ---    ---     ---     ---    ---        

Â&#x2014; 90 Â&#x2014;





  ' ''

    

 





 ---------  

  ------  

 -  --------    -----------------



 

   

  

-    ---     ---     ---   ----     

    

             

    

           

       

   -  

        ---     

   -  --- 





 -       - ---  ---  



    -     ---     ---      ----   

Â&#x2014; 91 Â&#x2014;


 

     

 

 

18. Ã&#x201A;îçâåäåíèå â ñòåïåíü ïðîèçâåäåíèÿ è ñòåïåíè                 

               

          

   

    ------    ---     ---   ---      



  ------   ---     ---   ---  

   

  

y

 

1

 

0 1

8%   8%    +,&+& & '  &  

+    +     +    

  -:      =     >  %           F %-'9"I, "                F "-'9"I,    % G,%"'\%#%  " G,%"'\ %#% " 

 ------  --------- 







  

 -----------------------------    "  

Â&#x2014; 92 Â&#x2014;

x

     !  !                      

                                  

  

  

  

 ),%( %'# F"-7(# 8%%'##'     )7(,# %$#  ! 0%'#      )7(,# < %$# ! +'#0   )7(,#<  %$# ! +'#0    )7(,#< %$# !

 ),%(, F""\    T\,# %$# !

Â&#x2014; 93 Â&#x2014;


 

     

 

 

18. Ã&#x201A;îçâåäåíèå â ñòåïåíü ïðîèçâåäåíèÿ è ñòåïåíè                 

               

          

   

    ------    ---     ---   ---      



  ------   ---     ---   ---  

   

  

y

 

1

 

0 1

8%   8%    +,&+& & '  &  

+    +     +    

  -:      =     >  %           F %-'9"I, "                F "-'9"I,    % G,%"'\%#%  " G,%"'\ %#% " 

 ------  --------- 







  

 -----------------------------    "  

Â&#x2014; 92 Â&#x2014;

x

     !  !                      

                                  

  

  

  

 ),%( %'# F"-7(# 8%%'##'     )7(,# %$#  ! 0%'#      )7(,# < %$# ! +'#0   )7(,#<  %$# ! +'#0    )7(,#< %$# !

 ),%(, F""\    T\,# %$# !

Â&#x2014; 93 Â&#x2014;


   T\,# %$# !

   

 T\,# %$#!

  

 T\,# %$#! 

  

  

 !  !      

  

                       ---      ---      ---  ---     

   ---  



    ---    ---     ---  ---   ---  ---  ---     

                     

                                                             

  

   

                        -  -------------------  --------    -----------------------



 







         

      

       

      

     

    

     

   

      

   

                               

         

Â&#x2014; 94 Â&#x2014;





  -  -------------------  --------   ----------------------

      











    -  ----------------  --------    ----------- 

          -  --------  ------  ---  --------------- --------------

       

  > > =   =  =       %                 )    )    )      -   -   

Â&#x2014; 95 Â&#x2014;


   T\,# %$# !

   

 T\,# %$#!

  

 T\,# %$#! 

  

  

 !  !      

  

                       ---      ---      ---  ---     

   ---  



    ---    ---     ---  ---   ---  ---  ---     

                     

                                                             

  

   

                        -  -------------------  --------    -----------------------



 







         

      

       

      

     

    

     

   

      

   

                               

         

Â&#x2014; 94 Â&#x2014;





  -  -------------------  --------   ----------------------

      











    -  ----------------  --------    ----------- 

          -  --------  ------  ---  --------------- --------------

       

  > > =   =  =       %                 )    )    )      -   -   

Â&#x2014; 95 Â&#x2014;


              

§ 7. Îäíî÷ëåíû 19. Îäíî÷ëåí è åãî ñòàíäàðòíûé âèä

  

     

 N

?

N  ?Y

N

N

? N

N N

N N

   % 

 N

?

?

N

N

?

J' % N'  % H.%   %   %





 G1II2'    G1II2'     G1II2'      G1II2'  ---    ---     G1II2' 



 ---    ---     ---     ---               

  +-'(  +-'(

+-'( [-'(

+-'( +-'(

T'.0-#-9'. % "  Q%2%%.0-#-9'. % "  G'.0-#-9'. % "    ---  

G1II2'      '('( ' (                     

  ---    

 ---   



 ---   ---  ---  ---  

    







 ---

 ---   ---    ---   ---   --- 

   







  

-     ---    ---  -----------------------

  -  

   ---   ---------------------

    ---    --- 

  --- 









 







   ---    ---

  ---  

 -  

   ---    –------------

    

    --- 

   

 

 -    ---    ---   ------  ---  ---  ---  ------  ---  ---  ------  ----       

–    -    

 ---------------------------

— 96 —





    ---  



– 

— 97 —




              

§ 7. Îäíî÷ëåíû 19. Îäíî÷ëåí è åãî ñòàíäàðòíûé âèä

  

     

 N

?

N  ?Y

N

N

? N

N N

N N

   % 

 N

?

?

N

N

?

J' % N'  % H.%   %   %





 G1II2'    G1II2'     G1II2'      G1II2'  ---    ---     G1II2' 



 ---    ---     ---     ---               

  +-'(  +-'(

+-'( [-'(

+-'( +-'(

T'.0-#-9'. % "  Q%2%%.0-#-9'. % "  G'.0-#-9'. % "    ---  

G1II2'      '('( ' (                     

  ---    

 ---   



 ---   ---  ---  ---  

    







 ---

 ---   ---    ---   ---   --- 

   







  

-     ---    ---  -----------------------

  -  

   ---   ---------------------

    ---    --- 

  --- 









 







   ---    ---

  ---  

 -  

   ---    –------------

    

    --- 

   

 

 -    ---    ---   ------  ---  ---  ---  ------  ---  ---  ------  ----       

–    -    

 ---------------------------

— 96 —





    ---  



– 

— 97 —








 



       



   ----------------- ---------------------- ------ ---- ----  



 







 

 





  









 





     -  ---------------------------  -----------------------------------  --------  ---  -----------------



   



20. Ã&#x201C;ìíîæåíèå îäíî÷ëåíîâ. Ã&#x201A;îçâåäåíèå îäíî÷ëåíà â ñòåïåíü 

  

   



  -    ---    ---  ---  --------------





 

    

  

 ---    ---    

                                                                          ---      ---     



 ---    ---     ---    ---     







           

Â&#x2014; 98 Â&#x2014;

                                        

      S                                                                 

                 

      

     

   

 ---    ---  



    

 -     ---    ----  



                                                

Â&#x2014; 99 Â&#x2014;






 



       



   ----------------- ---------------------- ------ ---- ----  



 







 

 





  









 





     -  ---------------------------  -----------------------------------  --------  ---  -----------------



   



20. Ã&#x201C;ìíîæåíèå îäíî÷ëåíîâ. Ã&#x201A;îçâåäåíèå îäíî÷ëåíà â ñòåïåíü 

  

   



  -    ---    ---  ---  --------------





 

    

  

 ---    ---    

                                                                          ---      ---     



 ---    ---     ---    ---     







           

Â&#x2014; 98 Â&#x2014;

                                        

      S                                                                 

                 

      

     

   

 ---    ---  



    

 -     ---    ----  



                                                

Â&#x2014; 99 Â&#x2014;


            

     ---        ---       ---   



    ---     



  ---   

                                                                              

  ---        ---       

  -    ---    ----

   --- '(   ' (   ---  ' (  ' ( 



 ---  '( ( '( 

             

Â&#x2014; 100 Â&#x2014;



  ! #!   #! " #!               

  



'('('('('(  '(    -    ------   ------       ---- 



 ),%( '5-,%,"( K.

+

T-,%

3%

 

  

 

33%



 













   ---      ---    









   ---    ---   ---  





 

     





 ------      ------------       ---        

    





 ' ' ' ' '

  



 - '   --- '   ------ '   ---  '  ------  ------ '' '  ----   

P'$ '33%,"$,#-!(4 %%#,#'' 

    

     

             ! '5  ),%( ! '5#3,# !I$'(4 #33 K.

+

)#!

36'7



   

 

336'7

 

   

  

P'$ #36'7I$,# !'(< 4 #33%%#,#''         

    

            !'5    %  "   

Â&#x2014; 101 Â&#x2014;


            

     ---        ---       ---   



    ---     



  ---   

                                                                              

  ---        ---       

  -    ---    ----

   --- '(   ' (   ---  ' (  ' ( 



 ---  '( ( '( 

             

Â&#x2014; 100 Â&#x2014;



  ! #!   #! " #!               

  



'('('('('(  '(    -    ------   ------       ---- 



 ),%( '5-,%,"( K.

+

T-,%

3%

 

  

 

33%



 













   ---      ---    









   ---    ---   ---  





 

     





 ------      ------------       ---        

    





 ' ' ' ' '

  



 - '   --- '   ------ '   ---  '  ------  ------ '' '  ----   

P'$ '33%,"$,#-!(4 %%#,#'' 

    

     

             ! '5  ),%( ! '5#3,# !I$'(4 #33 K.

+

)#!

36'7



   

 

336'7

 

   

  

P'$ #36'7I$,# !'(< 4 #33%%#,#''         

    

            !'5    %  "   

Â&#x2014; 101 Â&#x2014;


                            0'. -% '$ T'. 0-#-9'. %  Q%2%%. 0-#-9'. %  G'. 0-#-9'. %               

      

        

21. Ã&#x201D;óíêöèè O = N2 è O = N3 è èõ ãðà ôèêè     

  

  

   

     -     -         

  

    -     -       >'- -     ='- -           

 

 

      -    -     = '- -      > '- -    

Â&#x2014; 102 Â&#x2014;

 ),%(%'#%"-7( %  8% %' #  %  -7(     % )7(,# %$# ! 

  - %-7( --------- % 8%%'# ----



)7(,'(4%$#!

 *.-7(,# %(#!%',',#< (# ! *.-7(,# %(#!%',',#< (#!   



 

   -  -

     





         -  -  > >'--       8%,,# (# !\,# %$# ! 8%  , ,'(4( #  ! \ ,'(4%$ # !  &,',# (#!   

y



      

1 0

  

     - 

Â&#x2014; 103 Â&#x2014;

1

x


                            0'. -% '$ T'. 0-#-9'. %  Q%2%%. 0-#-9'. %  G'. 0-#-9'. %               

      

        

21. Ã&#x201D;óíêöèè O = N2 è O = N3 è èõ ãðà ôèêè     

  

  

   

     -     -         

  

    -     -       >'- -     ='- -           

 

 

      -    -     = '- -      > '- -    

Â&#x2014; 102 Â&#x2014;

 ),%(%'#%"-7( %  8% %' #  %  -7(     % )7(,# %$# ! 

  - %-7( --------- % 8%%'# ----



)7(,'(4%$#!

 *.-7(,# %(#!%',',#< (# ! *.-7(,# %(#!%',',#< (#!   



 

   -  -

     





         -  -  > >'--       8%,,# (# !\,# %$# ! 8%  , ,'(4( #  ! \ ,'(4%$ # !  &,',# (#!   

y



      

1 0

  

     - 

Â&#x2014; 103 Â&#x2014;

1

x


   

%  

       F %-'9"I,

    

  0'. -% '$

"   ---  --- 

   

          

F "-'9"I,

 M  MM M  M  MM M M  MMM M  MMM

  - #   ---  ----

   

        

     ------  ---  ---  ---

 ---   ---    ---    ---   





 -

 ---   ----





    ---   ------   

  -  ------  ---- 

             

  

    

      

 



F #'-'9"I,   

 

 

 



y

  

§ 8. Ã&#x20AC;áñîëþòíà ÿ è îòíîñèòåëüíàÿ ïîãðåøíîñòè



 

 =

22. Ã&#x20AC;áñîëþòíà ÿ ïîãðåøíîñòü

1 0

 > 

1

x

  > 

 )7(-,# %$# !-1,%-5<    "

     M M

     M M

    M M     M M

     M  M

    MM

 T\ ,# %$ #  ! -1, #' -,%$   ' 

     

  

M M M  M M   M

    > =   >   > =  >    

         

 

M  M M  M M  M M

 M

Â&#x2014; 104 Â&#x2014;

Â&#x2014; 105 Â&#x2014;


   

%  

       F %-'9"I,

    

  0'. -% '$

"   ---  --- 

   

          

F "-'9"I,

 M  MM M  M  MM M M  MMM M  MMM

  - #   ---  ----

   

        

     ------  ---  ---  ---

 ---   ---    ---    ---   





 -

 ---   ----





    ---   ------   

  -  ------  ---- 

             

  

    

      

 



F #'-'9"I,   

 

 

 



y

  

§ 8. Ã&#x20AC;áñîëþòíà ÿ è îòíîñèòåëüíàÿ ïîãðåøíîñòè



 

 =

22. Ã&#x20AC;áñîëþòíà ÿ ïîãðåøíîñòü

1 0

 > 

1

x

  > 

 )7(-,# %$# !-1,%-5<    "

     M M

     M M

    M M     M M

     M  M

    MM

 T\ ,# %$ #  ! -1, #' -,%$   ' 

     

  

M M M  M M   M

    > =   >   > =  >    

         

 

M  M M  M M  M M

 M

Â&#x2014; 104 Â&#x2014;

Â&#x2014; 105 Â&#x2014;


 ---  



     –

 ---    ---  ------  ---------------  ------  ------           –

 ---    ---  ---------  ---------------------  ---------  ---------           –

 ---    ---  ------------  ----------------------------  ------------  ------------      

    –

 --------  ---------  ---  ---------------------------







 

 %"# 584 % '%(:2.6  %5" % '%(:2.6 

A

M

B

  04'"'2,0%$.6  0'5502.6  00%.6  + -  ------   M  M>  ----------

)9'#.'% '%(: "  ---     ---  

 ---  

      –   -------- > ---------  ---------------------------          -   –  -  --------  ---------  ---  ------------------------------    

   ---------   ---------   ---------   0 -9'' !' ' % --   

%  '%(:

 ),%( ,%. 4 -4   " ' #,% 6     )4 ' -,( '#,%-6     P'$ #%(-,( %%#,#''                         ,%.4-4 

— 106 —

           -   ----------------------  ----------------------  ------------------------      --------------        



 

 



 

  -----------  ---------  ------  ------   ------  ---              -----------------  -----------------     

    --------------  --------------    

34'.#-,   '  334'.#-,  ' 34'' #9''(4 @ 0%%(34'. @ 0%%(334'. 334'-.#"'(4  F  -% '$ "I# !'   4'. #%%( !  -%' #9'$34'.' %%$'%

23. Îòíîñèòåëüíàÿ ïîãðåøíîñòü  -------   ------- /     M  M -------   /  -----------   /   M  M     M  M -------  /

  

  ---  

M  M

  M M

 -------------- / 

 -          -----

M   M    

  ----------------- /  

  –  -------------------------------  -------------- /  

   

 ----------- / 

  

 -----------   / 

  MM     M   M 

— 107 —


 ---  



     –

 ---    ---  ------  ---------------  ------  ------           –

 ---    ---  ---------  ---------------------  ---------  ---------           –

 ---    ---  ------------  ----------------------------  ------------  ------------      

    –

 --------  ---------  ---  ---------------------------







 

 %"# 584 % '%(:2.6  %5" % '%(:2.6 

A

M

B

  04'"'2,0%$.6  0'5502.6  00%.6  + -  ------   M  M>  ----------

)9'#.'% '%(: "  ---     ---  

 ---  

      –   -------- > ---------  ---------------------------          -   –  -  --------  ---------  ---  ------------------------------    

   ---------   ---------   ---------   0 -9'' !' ' % --   

%  '%(:

 ),%( ,%. 4 -4   " ' #,% 6     )4 ' -,( '#,%-6     P'$ #%(-,( %%#,#''                         ,%.4-4 

— 106 —

           -   ----------------------  ----------------------  ------------------------      --------------        



 

 



 

  -----------  ---------  ------  ------   ------  ---              -----------------  -----------------     

    --------------  --------------    

34'.#-,   '  334'.#-,  ' 34'' #9''(4 @ 0%%(34'. @ 0%%(334'. 334'-.#"'(4  F  -% '$ "I# !'   4'. #%%( !  -%' #9'$34'.' %%$'%

23. Îòíîñèòåëüíàÿ ïîãðåøíîñòü  -------   ------- /     M  M -------   /  -----------   /   M  M     M  M -------  /

  

  ---  

M  M

  M M

 -------------- / 

 -          -----

M   M    

  ----------------- /  

  –  -------------------------------  -------------- /  

   

 ----------- / 

  

 -----------   / 

  MM     M   M 

— 107 —


------- /   

 – 

------- /  -----------------------  



 -   /  ------------ 

 ----------- /  ------------------- /    

 

H!' '  " "   "  "

------------ /   ------------   /  

H!' '

 Q%2%% %'(4%2%%. "#! 







 





 





      -------------------  -----------------------------     



 



 

     -------------------  -----------------------------  --------------        

   

              0'. -% '$% %(:2%%  0'. -% '$% %(:'

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå III Ê ïàðàãðàôó 6                 &#'%#'#'            &#'%##'  )%(,-#!#' % ##< -,  %' #:7%$' T%:%,  9' #%$2I5

— 108 —

F    ' #%$2I5 )%9' %  -,  %' #:< 7%$'-%(,  T%%(!(  ' #%$' )1, %   ' #%$',!'< %$'                                             

  

   

    

   

                         

                           =    =    >  =  >  

> = 

>           = '        = '             =  '         

    =  '

— 109 —


------- /   

 – 

------- /  -----------------------  



 -   /  ------------ 

 ----------- /  ------------------- /    

 

H!' '  " "   "  "

------------ /   ------------   /  

H!' '

 Q%2%% %'(4%2%%. "#! 







 





 





      -------------------  -----------------------------     



 



 

     -------------------  -----------------------------  --------------        

   

              0'. -% '$% %(:2%%  0'. -% '$% %(:'

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå III Ê ïàðàãðàôó 6                 &#'%#'#'            &#'%##'  )%(,-#!#' % ##< -,  %' #:7%$' T%:%,  9' #%$2I5

— 108 —

F    ' #%$2I5 )%9' %  -,  %' #:< 7%$'-%(,  T%%(!(  ' #%$' )1, %   ' #%$',!'< %$'                                             

  

   

    

   

                         

                           =    =    >  =  >  

> = 

>           = '        = '             =  '         

    =  '

— 109 —


         =   =   =         >    >

 >

              

                         

           H%, $6-:',('%,2I %$,' -1, %''$ %< $' #%",$#$(%$',('. %     0'(  0'(    0'(   0'(     0'(  0'(      0'(   0'(       0'(   0'(      0'(           0'(  0'(  0'(        =     =  - :  %#(' ,#'' ''5    =-: %#(' ,#''   ''5

Â&#x2014; 110 Â&#x2014;

       P' '''"#.9'$#'-    )  =  #$ %( ,#''$ -9('    ' #' )1,-9('.6'5'  ?- >#$ %(,#''$-9('               



                 

     

             

        

    

    

 



 



 -      --------------  

        

    -  -------------  ---  -----------------



 

 

       

  -  ------  ---  -----------------  





         ---  ---  ---  --- 



  ---    

Â&#x2014; 111 Â&#x2014;






         =   =   =         >    >

 >

              

                         

           H%, $6-:',('%,2I %$,' -1, %''$ %< $' #%",$#$(%$',('. %     0'(  0'(    0'(   0'(     0'(  0'(      0'(   0'(       0'(   0'(      0'(           0'(  0'(  0'(        =     =  - :  %#(' ,#'' ''5    =-: %#(' ,#''   ''5

Â&#x2014; 110 Â&#x2014;

       P' '''"#.9'$#'-    )  =  #$ %( ,#''$ -9('    ' #' )1,-9('.6'5'  ?- >#$ %(,#''$-9('               



                 

     

             

        

    

    

 



 



 -      --------------  

        

    -  -------------  ---  -----------------



 

 

       

  -  ------  ---  -----------------  





         ---  ---  ---  --- 



  ---    

Â&#x2014; 111 Â&#x2014;






      8% ,% ," ,# ( #  !  -7( ,#< %$# ! 8%,%,",# (#!-< 7(,# %$# !  9 2 



  2  2    2  -  --------------------  ----------------   -----------------------

 2 

 2 



 ----------------  ------------  -----------------------       2 

T\,# %$# ! 92 T\,# %$#!  H' ?M M-:  (-  '-MM

    ---    ---   



                                      ---     ---     ---  

  ---    



  ---      

          > -1,>           =-1, =               > -1, >        = -1,= 

Â&#x2014; 112 Â&#x2014;

                                         



             

         

                              ' "    ' "   '"     ' "        



 2 



             

                       -   0 % '2('.  -  )%(,:$%-'( %' #< %$ '   V 9 %#5%# : 7 2I.           F   ' #%$ 2I5     ' #%$ '25     ',5

#$

+,:" %##$%$ '  -1,  %$'

Â&#x2014; 113 Â&#x2014;


      8% ,% ," ,# ( #  !  -7( ,#< %$# ! 8%,%,",# (#!-< 7(,# %$# !  9 2 



  2  2    2  -  --------------------  ----------------   -----------------------

 2 

 2 



 ----------------  ------------  -----------------------       2 

T\,# %$# ! 92 T\,# %$#!  H' ?M M-:  (-  '-MM

    ---    ---   



                                      ---     ---     ---  

  ---    



  ---      

          > -1,>           =-1, =               > -1, >        = -1,= 

Â&#x2014; 112 Â&#x2014;

                                         



             

         

                              ' "    ' "   '"     ' "        



 2 



             

                       -   0 % '2('.  -  )%(,:$%-'( %' #< %$ '   V 9 %#5%# : 7 2I.           F   ' #%$ 2I5     ' #%$ '25     ',5

#$

+,:" %##$%$ '  -1,  %$'

Â&#x2014; 113 Â&#x2014;


Ê ïàðàãðàôó 7

 

     %-'(

              

 

    

   

       --- 

    ---        %-'(

       %-'(    %-'(      %-'(     ---   %-'( 

------    ---    



    -----------------------------     





     -  -------    ---   ---   ---    ---   --------------------------









 





  

-   ---   ---     ---     ---   ------------------------------

  

      

  ---

   ---      ---  

   

 3   

    

    

 ---   ---     ---     ---       ---  

    

                

 



                  !  !  !                    

      

        ---                     --- 

    

    ------  ------  --------------------------------------------  

   ---     

          

                   

          

 

      













  

  -   ------    ---   ---    ---     ---     ----      





      ----------------------------------------------------   



— 114 —

         



   - ' ( --- '( ------ ' (    --- '(  ----  







            

— 115 —


Ê ïàðàãðàôó 7

 

     %-'(

              

 

    

   

       --- 

    ---        %-'(

       %-'(    %-'(      %-'(     ---   %-'( 

------    ---    



    -----------------------------     





     -  -------    ---   ---   ---    ---   --------------------------









 





  

-   ---   ---     ---     ---   ------------------------------

  

      

  ---

   ---      ---  

   

 3   

    

    

 ---   ---     ---     ---       ---  

    

                

 



                  !  !  !                    

      

        ---                     --- 

    

    ------  ------  --------------------------------------------  

   ---     

          

                   

          

 

      













  

  -   ------    ---   ---    ---     ---     ----      





      ----------------------------------------------------   



— 114 —

         



   - ' ( --- '( ------ ' (    --- '(  ----  







            

— 115 —


     

   ---       ---    

 

 -    ------   ---     ---    ---   ----  

                              

      

                        ---     ---    

    

   

  ---     ---    



   

 



   -         ---        ----





  -   ---         ---     -------



 

-    ------       ---      ---    ----  



      !   !

 ---    ---   

 6       7   F 7-'9"I,  =    =    =  >  >  >

— 116 —



  )%(, % -'9 "I, I,'2       F   "-'9"I, -%(, -1,#$",-'< 9("I,4(#%,   )%(, % -'9 "I, I,'2         F        "  # ' -'< 9"I,!%: '%, $ <  $-'9"I,-:.6  = = >>

> > >>

Ê ïàðàãðàôó 8   ---  

  ---  ------  

    –

---  ------   ---------------  ------  ------







       –

---  ---------  ---  ---------   ---------------------  ---------  --------- 







   ---  --------- 

     -  ----------–

-  ----------- ---  ------------   --------------------------





  -    ----      –  ------  ------  ------  ------   ------------------  – ---------  ------         

------  ---------  ------  ------   

   –

------  ------   ---------------------  ---------  ---------    

   ------  ------------  ---------     

   – -  – ----------------  ---------   -  ------------ -----------------------------       



– 

-    ------  ---------    -----------------------------  ------------ 

     



– 

------  ---------   -------------------------  ------------ = ------------  ------  ---------       

F '

— 117 —


     

   ---       ---    

 

 -    ------   ---     ---    ---   ----  

                              

      

                        ---     ---    

    

   

  ---     ---    



   

 



   -         ---        ----





  -   ---         ---     -------



 

-    ------       ---      ---    ----  



      !   !

 ---    ---   

 6       7   F 7-'9"I,  =    =    =  >  >  >

— 116 —



  )%(, % -'9 "I, I,'2       F   "-'9"I, -%(, -1,#$",-'< 9("I,4(#%,   )%(, % -'9 "I, I,'2         F        "  # ' -'< 9"I,!%: '%, $ <  $-'9"I,-:.6  = = >>

> > >>

Ê ïàðàãðàôó 8   ---  

  ---  ------  

    –

---  ------   ---------------  ------  ------







       –

---  ---------  ---  ---------   ---------------------  ---------  --------- 







   ---  --------- 

     -  ----------–

-  ----------- ---  ------------   --------------------------





  -    ----      –  ------  ------  ------  ------   ------------------  – ---------  ------         

------  ---------  ------  ------   

   –

------  ------   ---------------------  ---------  ---------    

   ------  ------------  ---------     

   – -  – ----------------  ---------   -  ------------ -----------------------------       



– 

-    ------  ---------    -----------------------------  ------------ 

     



– 

------  ---------   -------------------------  ------------ = ------------  ------  ---------       

F '

— 117 —


 

  ---  

------    

à ë à â à IV

F '

 MMM M>

ÌÍÎÃÎ×ËÅÍÛ

 -   ----

N%$.6 M M > N%.6 M ] > N.%$ '.6  M  M >  ---   

---         – ---  ------  ------------------  – -----  ------         –

------    ------  ------  ------  ------------------  – ------  ------       

+ ---  ------  ------------  ------      

  –   ---- ---- ---- 

------------------  ------  ------         -  ------ Q%:'.-"4'%%".6 ----  - Q%:'$-"4'%(%,. ----

– + –– ---------------      -------------------------  --------------- 

 +  – –    – – -  ---------------  -------------------------  ---------------  -------------

  –   –  --------------------------  --------------  -------     /      –    – -   /     ----------------------------------  ------------  ----------     

    

-------      

  -----------  ------   

)#!' '

/ T!' %:',:-"4'%(!'$ !  -     -------

 - %   &% ' %% %'% $ -------

— 118 —

§ 9. Ñóììà è ðàçíîñòü ìíîãî÷ëåíîâ 24. Ìíîãî÷ëåí è åãî ñòàíäàðòíûé âèä        0 ' #5%-'  0 '(5%-'   '-#5%-'  0 '',#5%-'%#'.5 '          '.(5%-'   '#5%-'

  '.-#5%-'   

             

                                                                                                    



                   '   ' '   '  ' ' ' '                              

— 119 —


 

  ---  

------    

à ë à â à IV

F '

 MMM M>

ÌÍÎÃÎ×ËÅÍÛ

 -   ----

N%$.6 M M > N%.6 M ] > N.%$ '.6  M  M >  ---   

---         – ---  ------  ------------------  – -----  ------         –

------    ------  ------  ------  ------------------  – ------  ------       

+ ---  ------  ------------  ------      

  –   ---- ---- ---- 

------------------  ------  ------         -  ------ Q%:'.-"4'%%".6 ----  - Q%:'$-"4'%(%,. ----

– + –– ---------------      -------------------------  --------------- 

 +  – –    – – -  ---------------  -------------------------  ---------------  -------------

  –   –  --------------------------  --------------  -------     /      –    – -   /     ----------------------------------  ------------  ----------     

    

-------      

  -----------  ------   

)#!' '

/ T!' %:',:-"4'%(!'$ !  -     -------

 - %   &% ' %% %'% $ -------

— 118 —

§ 9. Ñóììà è ðàçíîñòü ìíîãî÷ëåíîâ 24. Ìíîãî÷ëåí è åãî ñòàíäàðòíûé âèä        0 ' #5%-'  0 '(5%-'   '-#5%-'  0 '',#5%-'%#'.5 '          '.(5%-'   '#5%-'

  '.-#5%-'   

             

                                                                                                    



                   '   ' '   '  ' ' ' '                              

— 119 —


         

   

   

     

                                                                

                

                          

   

     

    

    F -:  =-:  ' %,7%#, " !' '$  -  !' ' '" '#'2('  -:  -: !'   = -:.6!' '$6   



                             [-'( [-'(

[-'( [-'(

[-'( [-'(

?-   ?-    

Â&#x2014; 120 Â&#x2014;

   

 

                       -  ------  ---------   ---      ----







 ---   ---  ---  ---

     â&#x20AC;&#x201C; 

â&#x20AC;&#x201C;  -  ---   ---  ---  --------------  ---------  ---  -----



 















      -  ------------------------  ----------------  ------  ---   -----------------



 

-  ----------------  ------   -----------





      -  ------------------------  -------------------  ---  --------------



  





        )  I,'2$-'!' '      ) I,'2$-'!' '              

25. Ã&#x2018;ëîæåíèå è âû÷èòà íèå ìíîãî÷ëåíîâ        

   

                                                                          

Â&#x2014; 121 Â&#x2014;


         

   

   

     

                                                                

                

                          

   

     

    

    F -:  =-:  ' %,7%#, " !' '$  -  !' ' '" '#'2('  -:  -: !'   = -:.6!' '$6   



                             [-'( [-'(

[-'( [-'(

[-'( [-'(

?-   ?-    

Â&#x2014; 120 Â&#x2014;

   

 

                       -  ------  ---------   ---      ----







 ---   ---  ---  ---

     â&#x20AC;&#x201C; 

â&#x20AC;&#x201C;  -  ---   ---  ---  --------------  ---------  ---  -----



 















      -  ------------------------  ----------------  ------  ---   -----------------



 

-  ----------------  ------   -----------





      -  ------------------------  -------------------  ---  --------------



  





        )  I,'2$-'!' '      ) I,'2$-'!' '              

25. Ã&#x2018;ëîæåíèå è âû÷èòà íèå ìíîãî÷ëåíîâ        

   

                                                                          

Â&#x2014; 121 Â&#x2014;


                                                                                                   

     

                           

  



  

                                       :                                               !!      !  !                   

5   

 

5 

    5  

Â&#x2014; 122 Â&#x2014;

5     5     5    5 5        

      

                                                                                                                                    

           

                                           ---   

      ---   

 -:!' ' 

= -:!' '

Â&#x2014; 123 Â&#x2014;


                                                                                                   

     

                           

  



  

                                       :                                               !!      !  !                   

5   

 

5 

    5  

Â&#x2014; 122 Â&#x2014;

5     5     5    5 5        

      

                                                                                                                                    

           

                                           ---   

      ---   

 -:!' ' 

= -:!' '

Â&#x2014; 123 Â&#x2014;


              

 





        N#, ' 

      

    

?-#''.66# N#, ' 

  ---         ---   

              ), ''#.9''!#% 1-< ''$#'%,%#,                              !                                                                              

   

                          --- 

                           



                    â&#x20AC;&#x201C;    ------   

Â&#x2014; 124 Â&#x2014;

          ---

                                

   

                                            

    

 -  â&#x20AC;&#x201C;---------â&#x20AC;&#x201C;

                                      

                          ''$%,-''#%  )"I,       M  MMM  â&#x20AC;&#x201C;    -  ----------- /  -----------------------------



     ---  ---    ---  ---          ---  ---       

 ---    





   --- 

 --- 





  ---     ---   

Â&#x2014; 125 Â&#x2014;


              

 





        N#, ' 

      

    

?-#''.66# N#, ' 

  ---         ---   

              ), ''#.9''!#% 1-< ''$#'%,%#,                              !                                                                              

   

                          --- 

                           



                    â&#x20AC;&#x201C;    ------   

Â&#x2014; 124 Â&#x2014;

          ---

                                

   

                                            

    

 -  â&#x20AC;&#x201C;---------â&#x20AC;&#x201C;

                                      

                          ''$%,-''#%  )"I,       M  MMM  â&#x20AC;&#x201C;    -  ----------- /  -----------------------------



     ---  ---    ---  ---          ---  ---       

 ---    





   --- 

 --- 





  ---     ---   

Â&#x2014; 125 Â&#x2014;


                          

 ---    ---   ---   --- 



                              ' ( '( '(  (' ( '(   ' (

 ---        

 ---    ---   ---  ---    ---  ---    --- 

 ---      ---   ---    

  ---     ---     ---    ---    ---   

    ---   --- 



— 126 —

               



                                          

 ---      





                                          ' ' ' ' ' '   '      

                



 ---       

                                1 1      



                                 ---     ---    --- 

26. Óìíîæåíèå îäíî÷ëåíà íà ìíîãî÷ëåí











§ 10. Ïðîèçâåäåíèå îäíî÷ëåíà è ìíîãî÷ëåíà

                       



                                          

                              

— 127 —


                          

 ---    ---   ---   --- 



                              ' ( '( '(  (' ( '(   ' (

 ---        

 ---    ---   ---  ---    ---  ---    --- 

 ---      ---   ---    

  ---     ---     ---    ---    ---   

    ---   --- 



— 126 —

               



                                          

 ---      





                                          ' ' ' ' ' '   '      

                



 ---       

                                1 1      



                                 ---     ---    --- 

26. Óìíîæåíèå îäíî÷ëåíà íà ìíîãî÷ëåí











§ 10. Ïðîèçâåäåíèå îäíî÷ëåíà è ìíîãî÷ëåíà

                       



                                          

                              

— 127 —


       

                                                                 

  

               

  

   

            

                                   

   ---       ---   

   ---      ---     

              S   S    )7(#%5I",. )7(3 % )7(33 % )7(#%5 I",.#'%,-75 %5%< %#$:76                                          

Â&#x2014; 128 Â&#x2014;

                                            -''-9('.!' '$-: >-1, >-:        

 

            

                

                          

  

 

              

                        

   

 

- 

   ----

        1                         1      

      





              

  

                       

   

   

  

Â&#x2014; 129 Â&#x2014;


       

                                                                 

  

               

  

   

            

                                   

   ---       ---   

   ---      ---     

              S   S    )7(#%5I",. )7(3 % )7(33 % )7(#%5 I",.#'%,-75 %5%< %#$:76                                          

Â&#x2014; 128 Â&#x2014;

                                            -''-9('.!' '$-: >-1, >-:        

 

            

                

                          

  

 

              

                        

   

 

- 

   ----

        1                         1      

      





              

  

                       

   

   

  

Â&#x2014; 129 Â&#x2014;


                           

   

 ---   

---   

------   ! !

!  !





   

     -----------  -----------   

    



------  --------   

 -------  ------- 

 

  

------------  ------------ 



  

Â&#x2014; 130 Â&#x2014;

        

  

â&#x20AC;&#x201C; â&#x20AC;&#x201C; ----------------  ------------    



               

 --- 

â&#x20AC;&#x201C;  -  ---    --------------

   

------   ---  

  

 



 

  

 

 â&#x20AC;&#x201C;  â&#x20AC;&#x201C;

-  ----------------    -----------



  ---





      

    

        

â&#x20AC;&#x201C; -    ---  ---------------

 

 



  ---

------  ---  

 ------  --------  --------   





!  ! ---

  



                 

 ------  ------    





 +  â&#x20AC;&#x201C;  -------------------  -------------------     

------  !   !

 ---

 

â&#x20AC;&#x201C;  â&#x20AC;&#x201C; ----------------  ----------------      

    

  --------  ---   

 ---  ---    







 --------  --------    





  

          

    

    

                             ---  --- 



 ------  ---  --- 

 

                     

     

 

    

 

   

-------------  ----------  --------  



  --------  -----  ---   

------     

  



+ + ----------------  ------------      



     

       

    ---   --- 

'+ â&#x20AC;&#x201C; ----------------  ------------- '  '  





' '' ' ' ' '

' ---  ' --- 

Â&#x2014; 131 Â&#x2014;


                           

   

 ---   

---   

------   ! !

!  !





   

     -----------  -----------   

    



------  --------   

 -------  ------- 

 

  

------------  ------------ 



  

Â&#x2014; 130 Â&#x2014;

        

  

â&#x20AC;&#x201C; â&#x20AC;&#x201C; ----------------  ------------    



               

 --- 

â&#x20AC;&#x201C;  -  ---    --------------

   

------   ---  

  

 



 

  

 

 â&#x20AC;&#x201C;  â&#x20AC;&#x201C;

-  ----------------    -----------



  ---





      

    

        

â&#x20AC;&#x201C; -    ---  ---------------

 

 



  ---

------  ---  

 ------  --------  --------   





!  ! ---

  



                 

 ------  ------    





 +  â&#x20AC;&#x201C;  -------------------  -------------------     

------  !   !

 ---

 

â&#x20AC;&#x201C;  â&#x20AC;&#x201C; ----------------  ----------------      

    

  --------  ---   

 ---  ---    







 --------  --------    





  

          

    

    

                             ---  --- 



 ------  ---  --- 

 

                     

     

 

    

 

   

-------------  ----------  --------  



  --------  -----  ---   

------     

  



+ + ----------------  ------------      



     

       

    ---   --- 

'+ â&#x20AC;&#x201C; ----------------  ------------- '  '  





' '' ' ' ' '

' ---  ' --- 

Â&#x2014; 131 Â&#x2014;


â&#x20AC;&#x201C; ----------------  ---  ----- 

â&#x20AC;&#x201C;

â&#x20AC;&#x201C; -------------------  ------------     

 





                 

  

 ---

 

+  â&#x20AC;&#x201C; ---------------  ---  ------------    



' +  â&#x20AC;&#x201C; ----------------  ----------------     '

          

          

â&#x20AC;&#x201C;

â&#x20AC;&#x201C; -  ------------   -----------





                         â&#x20AC;&#x201C;   +  -  -------  ------------  ---   --------------



 +     â&#x20AC;&#x201C;        ---------------------  ------------  -----------------  -----------   

            ------        

+ â&#x20AC;&#x201C; ---------------------   ------------     







 ---



 â&#x20AC;&#x201C; + ---------------------     ----------  ------------   

           

+ â&#x20AC;&#x201C; + -   ----------- ---------- -----------



 

           

     

 

  



 --- 

 ---

â&#x20AC;&#x201C;  +  -  ----------------       --------------



                        â&#x20AC;&#x201C;  â&#x20AC;&#x201C; ----------------  ----------------      

               

Â&#x2014; 132 Â&#x2014;





â&#x20AC;&#x201C;

â&#x20AC;&#x201C; -  -----------------          ----------------





          

 







â&#x20AC;&#x201C;

â&#x20AC;&#x201C;

---------------  ------------  --  



      

'  '  ''   '  '  '

 +  â&#x20AC;&#x201C;

-  -------------------  ---      --------------





              ------   ---     



 ),%(  0%%(#"'%   . 0   +%#,#''           

     '#%  ' 0    .0      ),%( ($ %'  % " #$  %  -#$   % P'$ -#'%%%#,#''

           S'.,"('#'.  %  ),%(#3'(-' #330 #333'(0       ---  #%" !  '$ -        

 ---           - ,%#: #'

   +%#

,#''  +   - 

   ---  

    -----------------------



   



 



 

 

--- 

  # 3 '( -   #75 # 33 0    # 333 0 

Â&#x2014; 133 Â&#x2014;


â&#x20AC;&#x201C; ----------------  ---  ----- 

â&#x20AC;&#x201C;

â&#x20AC;&#x201C; -------------------  ------------     

 





                 

  

 ---

 

+  â&#x20AC;&#x201C; ---------------  ---  ------------    



' +  â&#x20AC;&#x201C; ----------------  ----------------     '

          

          

â&#x20AC;&#x201C;

â&#x20AC;&#x201C; -  ------------   -----------





                         â&#x20AC;&#x201C;   +  -  -------  ------------  ---   --------------



 +     â&#x20AC;&#x201C;        ---------------------  ------------  -----------------  -----------   

            ------        

+ â&#x20AC;&#x201C; ---------------------   ------------     







 ---



 â&#x20AC;&#x201C; + ---------------------     ----------  ------------   

           

+ â&#x20AC;&#x201C; + -   ----------- ---------- -----------



 

           

     

 

  



 --- 

 ---

â&#x20AC;&#x201C;  +  -  ----------------       --------------



                        â&#x20AC;&#x201C;  â&#x20AC;&#x201C; ----------------  ----------------      

               

Â&#x2014; 132 Â&#x2014;





â&#x20AC;&#x201C;

â&#x20AC;&#x201C; -  -----------------          ----------------





          

 







â&#x20AC;&#x201C;

â&#x20AC;&#x201C;

---------------  ------------  --  



      

'  '  ''   '  '  '

 +  â&#x20AC;&#x201C;

-  -------------------  ---      --------------





              ------   ---     



 ),%(  0%%(#"'%   . 0   +%#,#''           

     '#%  ' 0    .0      ),%( ($ %'  % " #$  %  -#$   % P'$ -#'%%%#,#''

           S'.,"('#'.  %  ),%(#3'(-' #330 #333'(0       ---  #%" !  '$ -        

 ---           - ,%#: #'

   +%#

,#''  +   - 

   ---  

    -----------------------



   



 



 

 

--- 

  # 3 '( -   #75 # 33 0    # 333 0 

Â&#x2014; 133 Â&#x2014;


 ),%(#33%. %'"#3 0  H3%< %(  #33%   P'$ #33!< %( --- " %%(#3 %%%#,#'' 

  ---    

         

       #3% %'#33 0  ),%(-'(9'. #( 5 # %''% #( # % N'#'$ '#'

  +%#,#''  

   

  

       (9'. #(-'

    5#'(  ),%(-7(," """9'.!<

- '5! ------ '5 ''('(< ( ----

4 -'#%(-1,



 --------  --------   

   

 -7(,"#'"  ),%( ' %'2   +-%' 9' .

- '-"! --------- ' ' -"(! ------- 



 ''(4 +%#,#''



 ---------  ---------    

     

 '%'2    ),%(%%$'-# "'-,(-#<

   ' '.5 -,( ---    ' ---   ! ' ------  

(4 +%#,#''

   

  ------------  --------  ------------    

-  D2%!9#$-6 -6"! ----

%%$'#'    +%#,#''

+   

 --------  ---------------------   





 T!'  % %%$' !    H%-%

       

   

 #% -!4'%%$'%  ),%("#$4'!'-,(#%    " ",!#$ 0     ),(#% $"#5 4'.     $ ",!#5 0       +%# ,#''

          

   #% -!5'%%$'%        



          F -% '$   

   

    

         F -% '$     333Z #( 3333 #(

3333Z #( 33333Z #(

    



















y y = x2

B 1

F -% '$ % " 

â&#x20AC;&#x201C;2

 -#%''%%$' !.

Â&#x2014; 134 Â&#x2014;

y=4

4 A

Â&#x2014; 135 Â&#x2014;

0 1 2

x


 ),%(#33%. %'"#3 0  H3%< %(  #33%   P'$ #33!< %( --- " %%(#3 %%%#,#'' 

  ---    

         

       #3% %'#33 0  ),%(-'(9'. #( 5 # %''% #( # % N'#'$ '#'

  +%#,#''  

   

  

       (9'. #(-'

    5#'(  ),%(-7(," """9'.!<

- '5! ------ '5 ''('(< ( ----

4 -'#%(-1,



 --------  --------   

   

 -7(,"#'"  ),%( ' %'2   +-%' 9' .

- '-"! --------- ' ' -"(! ------- 



 ''(4 +%#,#''



 ---------  ---------    

     

 '%'2    ),%(%%$'-# "'-,(-#<

   ' '.5 -,( ---    ' ---   ! ' ------  

(4 +%#,#''

   

  ------------  --------  ------------    

-  D2%!9#$-6 -6"! ----

%%$'#'    +%#,#''

+   

 --------  ---------------------   





 T!'  % %%$' !    H%-%

       

   

 #% -!4'%%$'%  ),%("#$4'!'-,(#%    " ",!#$ 0     ),(#% $"#5 4'.     $ ",!#5 0       +%# ,#''

          

   #% -!5'%%$'%        



          F -% '$   

   

    

         F -% '$     333Z #( 3333 #(

3333Z #( 33333Z #(

    



















y y = x2

B 1

F -% '$ % " 

â&#x20AC;&#x201C;2

 -#%''%%$' !.

Â&#x2014; 134 Â&#x2014;

y=4

4 A

Â&#x2014; 135 Â&#x2014;

0 1 2

x


 

 























                    ' '' '  

         

    

y y = x2

B 1

 F -% '$ %" 

y = 2x

1 0 A 2

x

  ---       ---    



 ---    --- 

          

27. Ã&#x201A;ûíåñåíèå îáùåãî ìíîæèòåëÿ çà ñêîáêè           '  ' ' '                 





       

                                    

 

     

                     ' ( '('('(

Â&#x2014; 136 Â&#x2014;

           





           

     

                       

                                              

              ---                             -

       ----  ---   

 



 ---    

 ---  

 ---  



          -    ----

     

    

  ---  

   ---   

   ---   --- 



Â&#x2014; 137 Â&#x2014;


 

 























                    ' '' '  

         

    

y y = x2

B 1

 F -% '$ %" 

y = 2x

1 0 A 2

x

  ---       ---    



 ---    --- 

          

27. Ã&#x201A;ûíåñåíèå îáùåãî ìíîæèòåëÿ çà ñêîáêè           '  ' ' '                 





       

                                    

 

     

                     ' ( '('('(

Â&#x2014; 136 Â&#x2014;

           





           

     

                       

                                              

              ---                             -

       ----  ---   

 



 ---    

 ---  

 ---  



          -    ----

     

    

  ---  

   ---   

   ---   --- 



Â&#x2014; 137 Â&#x2014;


     

         

         

         

     

  

     

   

       T'!'95'%#('-!#< '' 





                                                                  )!#' %$ '  -1,  '' #.9' %$'                                                                                    

Â&#x2014; 138 Â&#x2014;

               

                                                           

                                              T75'9(            T75'9(     T75'9(     '' T75'9('

'' ' ' ' '' '   T75'9(      T75'9(                                                       

Â&#x2014; 139 Â&#x2014;


     

         

         

         

     

  

     

   

       T'!'95'%#('-!#< '' 





                                                                  )!#' %$ '  -1,  '' #.9' %$'                                                                                    

Â&#x2014; 138 Â&#x2014;

               

                                                           

                                              T75'9(            T75'9(     T75'9(     '' T75'9('

'' ' ' ' '' '   T75'9(      T75'9(                                                       

Â&#x2014; 139 Â&#x2014;


                               '  ('  '  (                                                ),%(%%$'%"#' "#$'-,(%"

- '#' ------ P'$ ''.5 ,#' ----



-,(! '' ---  '(4%%#,#'' 

 ------  ------  ---   



    

  %%$'%"#' 



   

                    

+  – 

-------------------  -------------------     



 

   

     

  ------   ---  ---  

   

   

–

        

  -  -----------   -----------

 

– 

     

  

— 140 —

28. Óìíîæåíèå ìíîãî÷ëåíà íà ìíîãî÷ëåí                                                                                            

  

      ' ''     

–  – ----------------  -------------------      

§ 11. Ïðîèçâåäåíèå ìíîãî÷ëåíîâ

  

        

                      )7(I",.#'%,-75 %5                                             

— 141 —


                               '  ('  '  (                                                ),%(%%$'%"#' "#$'-,(%"

- '#' ------ P'$ ''.5 ,#' ----



-,(! '' ---  '(4%%#,#'' 

 ------  ------  ---   



    

  %%$'%"#' 



   

                    

+  – 

-------------------  -------------------     



 

   

     

  ------   ---  ---  

   

   

–

        

  -  -----------   -----------

 

– 

     

  

— 140 —

28. Óìíîæåíèå ìíîãî÷ëåíà íà ìíîãî÷ëåí                                                                                            

  

      ' ''     

–  – ----------------  -------------------      

§ 11. Ïðîèçâåäåíèå ìíîãî÷ëåíîâ

  

        

                      )7(I",.#'%,-75 %5                                             

— 141 —


      '  ' '  ''  ' '  ' ' '                                                                                                   '' ' ''  '' '     ' ' '                                                       

               

 3            

Â&#x2014; 142 Â&#x2014;

                                                       

        

    ' '  '    '   '      '   '  '  '                                                                                                                                                          

    

Â&#x2014; 143 Â&#x2014;


      '  ' '  ''  ' '  ' ' '                                                                                                   '' ' ''  '' '     ' ' '                                                       

               

 3            

Â&#x2014; 142 Â&#x2014;

                                                       

        

    ' '  '    '   '      '   '  '  '                                                                                                                                                          

    

Â&#x2014; 143 Â&#x2014;


    

    

 

  

                                                       

   

    



                                                                                   

                                                                               

      ' ' ''   '  ' '  '  ' '

Â&#x2014; 144 Â&#x2014;

                                                         

                                      -:   = -:                                                            

 ---

  

                               

      

      

          

 

    

 --- 

Â&#x2014; 145 Â&#x2014;


    

    

 

  

                                                       

   

    



                                                                                   

                                                                               

      ' ' ''   '  ' '  '  ' '

Â&#x2014; 144 Â&#x2014;

                                                         

                                      -:   = -:                                                            

 ---

  

                               

      

      

          

 

    

 --- 

Â&#x2014; 145 Â&#x2014;


              

 

 -

 ----

 ---

                                     

               

   ---   --- 



                              ),%( %#'. P'$ #'(4" %' '(4-!#< '$#,6%('.6%%#,#''                    %     ),%( %#'.    )!#'(46     )!#''(46    P'$  !'%( 9, -!#'$  %%# ,#''                 

          %   

N'%

J'%

)7(%

K.

 

   

+



   

   

Â&#x2014; 146 Â&#x2014;

6   P'$ -7(,# %$' % %%#,#''                               4'-$,"('%' %  ),%(%'# %"%'.-$,"('<  %   % )7(# % -< 7(-$,"('   % P'$  -7( # '  %  '(4 %%# ,#''         

   %'# %  ),%( "   '5 " 9' . < (     '(  )'# !'     5  !"# 5 P'$ !"#'' < 5(4%%#,#''                    " '5  ),%( "   '5 !'  9' . ( '( )'#!'  "   " F"               

       "9'.#%-6( "  â&#x20AC;&#x201C; â&#x20AC;&#x201C; -  ---  ----------------     ----------





                    

+ â&#x20AC;&#x201C; ----------------  ------------    





                     

Â&#x2014; 147 Â&#x2014;


              

 

 -

 ----

 ---

                                     

               

   ---   --- 



                              ),%( %#'. P'$ #'(4" %' '(4-!#< '$#,6%('.6%%#,#''                    %     ),%( %#'.    )!#'(46     )!#''(46    P'$  !'%( 9, -!#'$  %%# ,#''                 

          %   

N'%

J'%

)7(%

K.

 

   

+



   

   

Â&#x2014; 146 Â&#x2014;

6   P'$ -7(,# %$' % %%#,#''                               4'-$,"('%' %  ),%(%'# %"%'.-$,"('<  %   % )7(# % -< 7(-$,"('   % P'$  -7( # '  %  '(4 %%# ,#''         

   %'# %  ),%( "   '5 " 9' . < (     '(  )'# !'     5  !"# 5 P'$ !"#'' < 5(4%%#,#''                    " '5  ),%( "   '5 !'  9' . ( '( )'#!'  "   " F"               

       "9'.#%-6( "  â&#x20AC;&#x201C; â&#x20AC;&#x201C; -  ---  ----------------     ----------





                    

+ â&#x20AC;&#x201C; ----------------  ------------    





                     

Â&#x2014; 147 Â&#x2014;


 +,## % G#%,. % &!'%(,# % G,!'% %

29. Ðàçëîæåíèå ìíîãî÷ëåíà íà ìíîæèòåëè ñïîñîáîì ãðóïïèðîâêè              ''' '((''('('(   3         

                                               

                                                                          

              

                                     

               ' ( '(('('( ' '(  '( ( '                                   ---    ---       ---   ---    ---  ---     ---  ---            

    + -  ---  ------  ------    ---  ---    ---  ---   ---   ---------- 













             ---    ---       ---    ---      ---  ---  

             ------      ---     ---   ---

    ---  ---            





                                                            

                              

                       '' ''  ;'  ' ; ''            

— 148 —

— 149 —


 +,## % G#%,. % &!'%(,# % G,!'% %

29. Ðàçëîæåíèå ìíîãî÷ëåíà íà ìíîæèòåëè ñïîñîáîì ãðóïïèðîâêè              ''' '((''('('(   3         

                                               

                                                                          

              

                                     

               ' ( '(('('( ' '(  '( ( '                                   ---    ---       ---   ---    ---  ---     ---  ---            

    + -  ---  ------  ------    ---  ---    ---  ---   ---   ---------- 













             ---    ---       ---    ---      ---  ---  

             ------      ---     ---   ---

    ---  ---            





                                                            

                              

                       '' ''  ;'  ' ; ''            

— 148 —

— 149 —


                                                                    



*%#

;5'5#.

H%"#'(

K.



  

   

+

 

 

P'$  9'#' % -, ( '    (4%%#,#''        

        % #  ),%("9'!"##( !5# %" '#'!'

!5 K"-!## %  !5!"#! %# !5 K"#.-'-'' / %%#$

 5    

          "9'!"##(!5#'(       



 

 

 ---

                  --- 

30. Ã&#x201E;îêà çàòåëüñòâî òîæäåñòâ                                   

Â&#x2014; 150 Â&#x2014;

  !  !   !  !   !  !   !  !                                                                                                                                          

                                       $    $                      $  $                                                 

         

Â&#x2014; 151 Â&#x2014;


                                                                    



*%#

;5'5#.

H%"#'(

K.



  

   

+

 

 

P'$  9'#' % -, ( '    (4%%#,#''        

        % #  ),%("9'!"##( !5# %" '#'!'

!5 K"-!## %  !5!"#! %# !5 K"#.-'-'' / %%#$

 5    

          "9'!"##(!5#'(       



 

 

 ---

                  --- 

30. Ã&#x201E;îêà çàòåëüñòâî òîæäåñòâ                                   

Â&#x2014; 150 Â&#x2014;

  !  !   !  !   !  !   !  !                                                                                                                                          

                                       $    $                      $  $                                                 

         

Â&#x2014; 151 Â&#x2014;


 

    

                  

    

   

                                                                                        

                                      &#'%#'$#$%$9%#                                  &#'%#'$#$%$9%#         &#'%#'$#$%$9%#                    &#'%#'$#$%$9%#

— 152 —

      

-  ---  ---  ---  ----  

 --- 

-

 ----





   



 

  

 

     ---

 –  + ----------------  ---------------     



      ) !' '-#"#.9'$''(4!' < '$#"  –  – ---------------  ---------------     

       )  %,5#'



  =0#'  >0''--    =   =0'-         

    

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå IV Ê ïàðàãðàôó 9     ---      

  ---   ---  ---  ---    ---   ---  ---  ---  ---  

 



 +



-  ------  –------------------



                       

— 153 —


 

    

                  

    

   

                                                                                        

                                      &#'%#'$#$%$9%#                                  &#'%#'$#$%$9%#         &#'%#'$#$%$9%#                    &#'%#'$#$%$9%#

— 152 —

      

-  ---  ---  ---  ----  

 --- 

-

 ----





   



 

  

 

     ---

 –  + ----------------  ---------------     



      ) !' '-#"#.9'$''(4!' < '$#"  –  – ---------------  ---------------     

       )  %,5#'



  =0#'  >0''--    =   =0'-         

    

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå IV Ê ïàðàãðàôó 9     ---      

  ---   ---  ---  ---    ---   ---  ---  ---  ---  

 



 +



-  ------  –------------------



                       

— 153 —


           ---           ---     ---     

   ---    

                       â&#x20AC;&#x201C;  !  !   !  !   !  !    ! 

! !  ---    ---        ---   ---  

    ---          

  

 ---     

        ):2 #.9'$   '. % ' ' +,:" %# '.6 %'" ' '"#%"' ' F62.6 '  8%  '    ' - '.6  #.9' #%" '  8%  ' '     ' %$ '    ' ' *%  '%,#,6' '.6 % #%"$#$%$ '. %-1,-' '.6 #.< 9'9 ' F62.6 '               



 

                                       

Â&#x2014; 154 Â&#x2014;

                                                                                                                            

    

   

    

                  %"#    #"%        %"##"%-,!''.6!' '$6%"#               ---  ---  ---  ---  ---  





            ---                   ---      

     

 

   ---    ---    ---   

 -:   -:    -:

Â&#x2014; 155 Â&#x2014;


           ---           ---     ---     

   ---    

                       â&#x20AC;&#x201C;  !  !   !  !   !  !    ! 

! !  ---    ---        ---   ---  

    ---          

  

 ---     

        ):2 #.9'$   '. % ' ' +,:" %# '.6 %'" ' '"#%"' ' F62.6 '  8%  '    ' - '.6  #.9' #%" '  8%  ' '     ' %$ '    ' ' *%  '%,#,6' '.6 % #%"$#$%$ '. %-1,-' '.6 #.< 9'9 ' F62.6 '               



 

                                       

Â&#x2014; 154 Â&#x2014;

                                                                                                                            

    

   

    

                  %"#    #"%        %"##"%-,!''.6!' '$6%"#               ---  ---  ---  ---  ---  





            ---                   ---      

     

 

   ---    ---    ---   

 -:   -:    -:

Â&#x2014; 155 Â&#x2014;


   ---     ---   ---  ---    



   ---   ---   ---  --- 





           -:    -:   > -:

    

   

       

                                                



 ---  ---  ---   ---  ---  --- 



 ---  ---  ---   ---  ---  --- 





 ---  --- 



 ---    ---    --- 

                    

     ),%( 1II2'--2'('%"%. %#'.   P'$!'%(9,#,$-< %'#,$-#. %%%#,#''            %    

— 156 —

 ),%(' % 8%',--%(%-#2I,  -,  %#'  +%##,#''             ' %  ),%(' % 8%',--%(%#2I,  ',# %$'  +%#,#''    

   

    ' %   ),%(-#.#2I.''" %%%#$: % F"'' %#' -, ''#' +%#,#''         

 

    ' %

Ê ïàðàãðàôó 10       

     



         

 ---   ---  ---    ---   ---  ---   

 ),%(!,' % )-%(',0!' ,< '9("' +%#,#''        !,' %

   ---   ---  ---   



                                                                       

— 157 —


   ---     ---   ---  ---    



   ---   ---   ---  --- 





           -:    -:   > -:

    

   

       

                                                



 ---  ---  ---   ---  ---  --- 



 ---  ---  ---   ---  ---  --- 





 ---  --- 



 ---    ---    --- 

                    

     ),%( 1II2'--2'('%"%. %#'.   P'$!'%(9,#,$-< %'#,$-#. %%%#,#''            %    

— 156 —

 ),%(' % 8%',--%(%-#2I,  -,  %#'  +%##,#''             ' %  ),%(' % 8%',--%(%#2I,  ',# %$'  +%#,#''    

   

    ' %   ),%(-#.#2I.''" %%%#$: % F"'' %#' -, ''#' +%#,#''         

 

    ' %

Ê ïàðàãðàôó 10       

     



         

 ---   ---  ---    ---   ---  ---   

 ),%(!,' % )-%(',0!' ,< '9("' +%#,#''        !,' %

   ---   ---  ---   



                                                                       

— 157 —


 #330   " F#3"%#< %%(# !(4 #33            

                  #3",-#! " %##33 0

"

              

 -:  = -:      ---    







 

  

-:  

 >

-:   ' --- 

-:



     ---      ---    ---         ---  

  ---   ---   --- 





 â&#x20AC;&#x201C;     â&#x20AC;&#x201C;   + 

---------------------  -------------------  ------------------------   

          

 



 



       ),%(#33%!#! #%"#3%!#!  #% H3% !   %%(     #33%%%(     P'$ #33% %%(' '(4%%#,#''                            #33%!#! #3 0   ),%( # 3 ", -#!  " %# " # 33 0   " *! #3"%%(  "

Â&#x2014; 158 Â&#x2014;

+

L!5#8





 --

     ---   

L!8#5



 

    ---       ---      ---  







     

-  ------  ------   ------ 

 ---    ---   --------------------





   



    +

-  --------  ------------  ------  -- -----

               

&:

P'$ -,(9,-%'$#' %%# ,#''

 +  

 â&#x20AC;&#x201C;   

+   â&#x20AC;&#x201C;  +  + ----------------   -------------------  ------------ ---------------------   ------------------------   ------------------   

 

,@



          

          

                                               

 â&#x20AC;&#x201C;

+ 

â&#x20AC;&#x201C; 

-  -------------------  -------------------   ---------------

F-6













---    ' 





 #% -!5 !   '  

,:@

&:

+:

3-6





33-6





 --

     ---   

),(-5''.5-6'9      ---       

   

     ---   ---  ---  ---    ---   





 #5-6"'-#.5 !   '%< %$' % 

Â&#x2014; 159 Â&#x2014;


 #330   " F#3"%#< %%(# !(4 #33            

                  #3",-#! " %##33 0

"

              

 -:  = -:      ---    







 

  

-:  

 >

-:   ' --- 

-:



     ---      ---    ---         ---  

  ---   ---   --- 





 â&#x20AC;&#x201C;     â&#x20AC;&#x201C;   + 

---------------------  -------------------  ------------------------   

          

 



 



       ),%(#33%!#! #%"#3%!#!  #% H3% !   %%(     #33%%%(     P'$ #33% %%(' '(4%%#,#''                            #33%!#! #3 0   ),%( # 3 ", -#!  " %# " # 33 0   " *! #3"%%(  "

Â&#x2014; 158 Â&#x2014;

+

L!5#8





 --

     ---   

L!8#5



 

    ---       ---      ---  







     

-  ------  ------   ------ 

 ---    ---   --------------------





   



    +

-  --------  ------------  ------  -- -----

               

&:

P'$ -,(9,-%'$#' %%# ,#''

 +  

 â&#x20AC;&#x201C;   

+   â&#x20AC;&#x201C;  +  + ----------------   -------------------  ------------ ---------------------   ------------------------   ------------------   

 

,@



          

          

                                               

 â&#x20AC;&#x201C;

+ 

â&#x20AC;&#x201C; 

-  -------------------  -------------------   ---------------

F-6













---    ' 





 #% -!5 !   '  

,:@

&:

+:

3-6





33-6





 --

     ---   

),(-5''.5-6'9      ---       

   

     ---   ---  ---  ---    ---   





 #5-6"'-#.5 !   '%< %$' % 

Â&#x2014; 159 Â&#x2014;




,:@

&

+:

3#,%

  --

  ---

33#,%



  --

  ---  

P'$ 3#,%'6%$"'%%$'#'

P'$  %%$' -  ': #  ! (4  -#%%#,#''             

  

    %%(#%$ 5# @  ),%( @ 0%%( '$ ,:@

&:

+:

 --- %%$'$%"%%#,#'' 

) ':

 



  

 ---   ---  ---  ---  

)# '$

 



  



------   ---  ---  ---  ---  ---     ----  

 -  ---    ----





  ------  ---   

@ 



  ------  ---------   



 

 ---  

 %%('"#,% @ ,"" 0@ &%%$'      ' --- 

),%( @ 0%%(-#"2%"%< %( #" 0   @  )#.5 -6 ---  

 #5 0 ---      -  # 1 -,( #6 

   0%%$'%" +%#,#'' ---    ---           

      @          %%( -#" 2%  @  #" 0  @ #% -!4# "  ),%( @ 0%%(#%$ 5# ,:@

&:

+:

) ':





  

)# '$



  

Â&#x2014; 160 Â&#x2014;

P'$  -,( -  ': '   '(4 %%# ,#''                     %%( '$  @  ),%(-#9'.#.-,%( % #'( )-',! '59'.#.-,%(

%  H.-,< %$#'(- % -#!'5#.-,%<  %  +%#,#''

 

     -#9'.#.-,%(#'(%   ),%(-#"%. "-4'2.#"% .  )%-#"%%%(   #" 0   +%#,#'' 

   

             -#"%-4'2..#"0   ),%("9'.( '5"-'< #!'  " &" '5,<   " P'$ %%(,("-, 

             "  "9'.,( "          

Â&#x2014; 161 Â&#x2014;




,:@

&

+:

3#,%

  --

  ---

33#,%



  --

  ---  

P'$ 3#,%'6%$"'%%$'#'

P'$  %%$' -  ': #  ! (4  -#%%#,#''             

  

    %%(#%$ 5# @  ),%( @ 0%%( '$ ,:@

&:

+:

 --- %%$'$%"%%#,#'' 

) ':

 



  

 ---   ---  ---  ---  

)# '$

 



  



------   ---  ---  ---  ---  ---     ----  

 -  ---    ----





  ------  ---   

@ 



  ------  ---------   



 

 ---  

 %%('"#,% @ ,"" 0@ &%%$'      ' --- 

),%( @ 0%%(-#"2%"%< %( #" 0   @  )#.5 -6 ---  

 #5 0 ---      -  # 1 -,( #6 

   0%%$'%" +%#,#'' ---    ---           

      @          %%( -#" 2%  @  #" 0  @ #% -!4# "  ),%( @ 0%%(#%$ 5# ,:@

&:

+:

) ':





  

)# '$



  

Â&#x2014; 160 Â&#x2014;

P'$  -,( -  ': '   '(4 %%# ,#''                     %%( '$  @  ),%(-#9'.#.-,%( % #'( )-',! '59'.#.-,%(

%  H.-,< %$#'(- % -#!'5#.-,%<  %  +%#,#''

 

     -#9'.#.-,%(#'(%   ),%(-#"%. "-4'2.#"% .  )%-#"%%%(   #" 0   +%#,#'' 

   

             -#"%-4'2..#"0   ),%("9'.( '5"-'< #!'  " &" '5,<   " P'$ %%(,("-, 

             "  "9'.,( "          

Â&#x2014; 161 Â&#x2014;


         

  



   0%$'  ''9(%$'                                                         %$' #-!#< ' '9('       '9('                                                                                  )               )      

              

 ---   ---   ---

  





    

Â&#x2014; 162 Â&#x2014;





 

 

 --- 



      

       





      ------   ---    

      

                         '''' '  '   ( ( (        8%  '     '  % 9  ' '    '-<-9','    8% ' '%9' ' ' -!#'-<-9',, '. %  &%%#,!' ' % 8% " 2I. !-%( # ' -$ -, %$ % L6%,#'    %$' N$6!' '.6 %'" '$%,#'      V %'%$'!%: '%, $" 

Â&#x2014; 163 Â&#x2014;


         

  



   0%$'  ''9(%$'                                                         %$' #-!#< ' '9('       '9('                                                                                  )               )      

              

 ---   ---   ---

  





    

Â&#x2014; 162 Â&#x2014;





 

 

 --- 



      

       





      ------   ---    

      

                         '''' '  '   ( ( (        8%  '     '  % 9  ' '    '-<-9','    8% ' '%9' ' ' -!#'-<-9',, '. %  &%%#,!' ' % 8% " 2I. !-%( # ' -$ -, %$ % L6%,#'    %$' N$6!' '.6 %'" '$%,#'      V %'%$'!%: '%, $" 

Â&#x2014; 163 Â&#x2014;


          $ #%6  ' '$ %  1 % '  %$ '    %$'       $#%6' '$%1 %%$' '  %$'

                                       

Ê ïàðàãðàôó 11

        

      1             !!!! !! !                                                                                                                                                                         

— 164 —

                                                                                                                                          

 >

               0%$'                                            

— 165 —


          $ #%6  ' '$ %  1 % '  %$ '    %$'       $#%6' '$%1 %%$' '  %$'

                                       

Ê ïàðàãðàôó 11

        

      1             !!!! !! !                                                                                                                                                                         

— 164 —

                                                                                                                                          

 >

               0%$'                                            

— 165 —


                                  "(( (     ( )                                )                        

 



 

                          



                              ),%( %#'.  P'$ -!#'-#.6#,6' '(4-!#< '$#,6%,:76%%#,#''             %  

  

 ),%( %#'.            ),%( %#'.                                  

Â&#x2014; 166 Â&#x2014;

 ),%(%'# %"%'.-$,"('       % )7(#  % -7( -$,"('        %  P'$  -7( #' % '(4-7-$,"('%< %#,#''             

            -7(# %  ),%( %' #  % " %'. -$,"(< '    % )7(# %  -< 7(-$,"('   % P'$ -7( # '  %  (4 -7 -$,"(' %< %#,#''

           %   %

0%'.-$,"('

  -7(-$,"('#'  %   6  ' 4'    ),%('-$,"(' "4'   -7(    )%!''$4'0   '  -7(    P'$ -7(,# %$ ' %%#,#''            

     N'-$,"('4'    -7(-$,"('#'    ),%('-$,"(' %"4'  % -7(   % )%!''$' %4'   % -7(   % P'$ -7(,'(4%$' % %%#,#''

               

        %      %    -7(-$,"('  %

Â&#x2014; 167 Â&#x2014;


                                  "(( (     ( )                                )                        

 



 

                          



                              ),%( %#'.  P'$ -!#'-#.6#,6' '(4-!#< '$#,6%,:76%%#,#''             %  

  

 ),%( %#'.            ),%( %#'.                                  

Â&#x2014; 166 Â&#x2014;

 ),%(%'# %"%'.-$,"('       % )7(#  % -7( -$,"('        %  P'$  -7( #' % '(4-7-$,"('%< %#,#''             

            -7(# %  ),%( %' #  % " %'. -$,"(< '    % )7(# %  -< 7(-$,"('   % P'$ -7( # '  %  (4 -7 -$,"(' %< %#,#''

           %   %

0%'.-$,"('

  -7(-$,"('#'  %   6  ' 4'    ),%('-$,"(' "4'   -7(    )%!''$4'0   '  -7(    P'$ -7(,# %$ ' %%#,#''            

     N'-$,"('4'    -7(-$,"('#'    ),%('-$,"(' %"4'  % -7(   % )%!''$' %4'   % -7(   % P'$ -7(,'(4%$' % %%#,#''

               

        %      %    -7(-$,"('  %

Â&#x2014; 167 Â&#x2014;


   )               )                       )           )                         )                  )                                                                                   

                                 '' ''                                       

Â&#x2014; 168 Â&#x2014;

                   

              

                

                                                                                                                                               -1,              -1,              -1,            -1,                         

Â&#x2014; 169 Â&#x2014;


   )               )                       )           )                         )                  )                                                                                   

                                 '' ''                                       

Â&#x2014; 168 Â&#x2014;

                   

              

                

                                                                                                                                               -1,              -1,              -1,            -1,                         

Â&#x2014; 169 Â&#x2014;


Ãëàâà V ÔÎÐÌÓËÛ ÑÎÊÐÀÙÅÍÍÎÃÎ ÓÌÍÎÆÅÍÈß

)7(#%%'5#'-7 # % %'5  ! ,#''5 -7 -$< ,"('-:%-7(#%%'5 !  ! (  (                                           

§ 12. Êâàäðàò ñóììû è êâàäðàò ðàçíîñòè 31. Âîçâåäåíèå â êâàäðàò ñóììû è ðàçíîñòè äâóõ âûðàæåíèé        '( '  '((                                 

                  

                             

  

                       

                  )7(I",.#'%,-75 %5%< %#$:76      

— 170 —

    ---       ---   ---  

 -     ----

 -     ---     ---   ---   ----   

           

                                   

  ---     ---    ---     ---     

 -    ---     ---   ---    ----



                                    !  !  !   ! !                              

— 171 —


Ãëàâà V ÔÎÐÌÓËÛ ÑÎÊÐÀÙÅÍÍÎÃÎ ÓÌÍÎÆÅÍÈß

)7(#%%'5#'-7 # % %'5  ! ,#''5 -7 -$< ,"('-:%-7(#%%'5 !  ! (  (                                           

§ 12. Êâàäðàò ñóììû è êâàäðàò ðàçíîñòè 31. Âîçâåäåíèå â êâàäðàò ñóììû è ðàçíîñòè äâóõ âûðàæåíèé        '( '  '((                                 

                  

                             

  

                       

                  )7(I",.#'%,-75 %5%< %#$:76      

— 170 —

    ---       ---   ---  

 -     ----

 -     ---     ---   ---   ----   

           

                                   

  ---     ---    ---     ---     

 -    ---     ---   ---    ----



                                    !  !  !   ! !                              

— 171 —


                                

  

  

        

       

    

      M   MM M     Q%:'$ -"4'%( #'  '%('$   -----------------  ------------ 

  

   --- '(    --- '    --- '((    

    Q%:'$ -"4'%( #'  '%('$

 ------ ' '((  --- ' '((  

 -----------------    

                            

    Q%:'$ -"4'%( #'   '%('$

                

  

  

     



 -----------------   

 @   Q%:'$ -"4'%( #'   '%('$  -----------------------   

     Q%:'$ -"4'%( #'   '%('$ 

-----------------    

    -       ------   ------       ----  



  

Q%:'$ -"4'%( #'  '%('$

 -    ---  --------

 -----------------------  





 



 '(  '   '((   ' '(( 

  

  

              

      

    

  



Â&#x2014; 172 Â&#x2014;

                 '( '  '((  ' '((                

  ---      ---     ---           ---    

Â&#x2014; 173 Â&#x2014;


                                

  

  

        

       

    

      M   MM M     Q%:'$ -"4'%( #'  '%('$   -----------------  ------------ 

  

   --- '(    --- '    --- '((    

    Q%:'$ -"4'%( #'  '%('$

 ------ ' '((  --- ' '((  

 -----------------    

                            

    Q%:'$ -"4'%( #'   '%('$

                

  

  

     



 -----------------   

 @   Q%:'$ -"4'%( #'   '%('$  -----------------------   

     Q%:'$ -"4'%( #'   '%('$ 

-----------------    

    -       ------   ------       ----  



  

Q%:'$ -"4'%( #'  '%('$

 -    ---  --------

 -----------------------  





 



 '(  '   '((   ' '(( 

  

  

              

      

    

  



Â&#x2014; 172 Â&#x2014;

                 '( '  '((  ' '((                

  ---      ---     ---           ---    

Â&#x2014; 173 Â&#x2014;


         

  ---     ---     ---      ---   

                         

                  

   

     

  

                                        

   ---       ---     ---       

-   ----   

          

   ---      ---    ---    





-      ---- 

    ---       ---   ---   ---    







-       ----

                                                                

          

     

Â&#x2014; 174 Â&#x2014;

                               

                                                  

                                                                                                   )                  )       

Â&#x2014; 175 Â&#x2014;


         

  ---     ---     ---      ---   

                         

                  

   

     

  

                                        

   ---       ---     ---       

-   ----   

          

   ---      ---    ---    





-      ---- 

    ---       ---   ---   ---    







-       ----

                                                                

          

     

Â&#x2014; 174 Â&#x2014;

                               

                                                  

                                                                                                   )                  )       

Â&#x2014; 175 Â&#x2014;


                    )                )          

      

  

 

        

   

  

   -

  

  

   ---- 

      

     

                                                      

   



 

                                                                                                                                                  

                   

                       

           

                

              

-



      ----

  ---     ---                                                    

Â&#x2014; 176 Â&#x2014;

            

     

  

                        +,##-!#'5 % %  G#%,.-!#'5 % % 

Â&#x2014; 177 Â&#x2014;


                    )                )          

      

  

 

        

   

  

   -

  

  

   ---- 

      

     

                                                      

   



 

                                                                                                                                                  

                   

                       

           

                

              

-



      ----

  ---     ---                                                    

Â&#x2014; 176 Â&#x2014;

            

     

  

                        +,##-!#'5 % %  G#%,.-!#'5 % % 

Â&#x2014; 177 Â&#x2014;


G#!'%-!#'5 % %  &!'%(##-!#'5 % % 

       

                                1           



          

                  

        

 

        

 ),%(%%('"-! @ ,"" @ +%(%9'$#'  @ ),(-5< ''.5!  #'   P'$#%(-,(%%#,#''                        %%('"-! @ ,""0 @

32. Ðàçëîæåíèå íà ìíîæèòåëè ñ ïîìîùüþ ôîðìóë êâàäðàòà ñóììû è êâàäðàòà ðàçíîñòè            !! !

'  '(( '(      

          1          

            

 ---          ---       ---         

  ---  

              

   -     ---   ---       ----  



   ---  

— 178 —



    ---    ---   

     ---       ---                     

         ^ ^        ^                ^ '( ( ^ ('(   '  (' ( '(                                   %       

  

                              

                   



           

— 179 —


G#!'%-!#'5 % %  &!'%(##-!#'5 % % 

       

                                1           



          

                  

        

 

        

 ),%(%%('"-! @ ,"" @ +%(%9'$#'  @ ),(-5< ''.5!  #'   P'$#%(-,(%%#,#''                        %%('"-! @ ,""0 @

32. Ðàçëîæåíèå íà ìíîæèòåëè ñ ïîìîùüþ ôîðìóë êâàäðàòà ñóììû è êâàäðàòà ðàçíîñòè            !! !

'  '(( '(      

          1          

            

 ---          ---       ---         

  ---  

              

   -     ---   ---       ----  



   ---  

— 178 —



    ---    ---   

     ---       ---                     

         ^ ^        ^                ^ '( ( ^ ('(   '  (' ( '(                                   %       

  

                              

                   



           

— 179 —


                            

 ---      ---    ---       

  ---   

  =-:.6  =              ?#'%# '#'  - !' '#.9'$#'

                    

                 

  ---    ---  ---    ---     ---  ---     

         

  

    = 

               

  

     

 

            

             G#!'% &!'%(## )!#'%,.'6!'%(

    ---   

     -  ------   ---    ---  ---  ------   ---  ----  





   

  ---  ---  

        

       0'(!$

  !  ! '(!$

    -     ---     ---      ---    ----    







  

           

    -     ---    ---    ----  



  --- 



Â&#x2014; 180 Â&#x2014;



   ---  

            '  ''  ' 0'(!$





   ---    ---    ---   

            

  ---     ---    ---    ---   

 -    ------    -----

  

 

 

       

      

                      

           

           

Â&#x2014; 181 Â&#x2014;


                            

 ---      ---    ---       

  ---   

  =-:.6  =              ?#'%# '#'  - !' '#.9'$#'

                    

                 

  ---    ---  ---    ---     ---  ---     

         

  

    = 

               

  

     

 

            

             G#!'% &!'%(## )!#'%,.'6!'%(

    ---   

     -  ------   ---    ---  ---  ------   ---  ----  





   

  ---  ---  

        

       0'(!$

  !  ! '(!$

    -     ---     ---      ---    ----    







  

           

    -     ---    ---    ----  



  --- 



Â&#x2014; 180 Â&#x2014;



   ---  

            '  ''  ' 0'(!$





   ---    ---    ---   

            

  ---     ---    ---    ---   

 -    ------    -----

  

 

 

       

      

                      

           

           

Â&#x2014; 181 Â&#x2014;


§ 13. Ðàçíîñòü êâàäðàòîâ. Ñóììà è ðàçíîñòü êóáîâ 33. Óìíîæåíèå ðàçíîñòè äâóõ âûðàæåíèé íà èõ ñóììó        '('(' (   ' ' '      

         

                         '''                

                    )7( -$,"(' % %'        #'!'%-75#%%'5#< %%'5                                       

                 

                

                

— 182 —

          

                             

           ---  ---    ---  ---     ---     ---         



-  ------   ----



                          

------    ---      ---       ---   



   

          

  

 

 

    

  

     



         

                     

    

      

    

 

         

   11 1 1 1         

— 183 —


§ 13. Ðàçíîñòü êâàäðàòîâ. Ñóììà è ðàçíîñòü êóáîâ 33. Óìíîæåíèå ðàçíîñòè äâóõ âûðàæåíèé íà èõ ñóììó        '('(' (   ' ' '      

         

                         '''                

                    )7( -$,"(' % %'        #'!'%-75#%%'5#< %%'5                                       

                 

                

                

— 182 —

          

                             

           ---  ---    ---  ---     ---     ---         



-  ------   ----



                          

------    ---      ---       ---   



   

          

  

 

 

    

  

     



         

                     

    

      

    

 

         

   11 1 1 1         

— 183 —


1 1 1 1 1   1  1    1  1    1 1      11   1      1      

                  1         

 '  ' ' ' '     ''   ''                                                                        1   1                   1   1 1 1 1 1         

     

                       

                  

                       

Â&#x2014; 184 Â&#x2014;

 

 

                                     11                                                                              1    1     ),%( %#'.  1 1

        1 1 11                    

                                                                            

   

  

   

                       

Â&#x2014; 185 Â&#x2014;


1 1 1 1 1   1  1    1  1    1 1      11   1      1      

                  1         

 '  ' ' ' '     ''   ''                                                                        1   1                   1   1 1 1 1 1         

     

                       

                  

                       

Â&#x2014; 184 Â&#x2014;

 

 

                                     11                                                                              1    1     ),%( %#'.  1 1

        1 1 11                    

                                                                            

   

  

   

                       

Â&#x2014; 185 Â&#x2014;


                         '(( ''('(' ( ' (  ' ( ' ( '                    

     

 





– -  ---          ----------

   

     

+ + ----------------          

 -----------





   



       – -   ---        ----------



           – ----------------    

     

   

   

  

                     

         

    

+

-         ---------------

    

 



    

    

 

    

           

 ---     ---   

–     --------------

    



        ),%(%%('"-! @  ,""  @ +%( %9'$     @  ),( -5''.5 !  ,#'    P'$#%(-,(%%#,#''                     %%('"-! @ ,"" @

                                            

— 186 —

34. Ðàçëîæåíèå ðàçíîñòè êâàäðàòîâ íà ìíîæèòåëè          ! !!                   

< <   < <       : 

     

— 187 —


                         '(( ''('(' ( ' (  ' ( ' ( '                    

     

 





– -  ---          ----------

   

     

+ + ----------------          

 -----------





   



       – -   ---        ----------



           – ----------------    

     

   

   

  

                     

         

    

+

-         ---------------

    

 



    

    

 

    

           

 ---     ---   

–     --------------

    



        ),%(%%('"-! @  ,""  @ +%( %9'$     @  ),( -5''.5 !  ,#'    P'$#%(-,(%%#,#''                     %%('"-! @ ,"" @

                                            

— 186 —

34. Ðàçëîæåíèå ðàçíîñòè êâàäðàòîâ íà ìíîæèòåëè          ! !!                   

< <   < <       : 

     

— 187 —


  ---     ---     ---    ---   



  ---     ---     ---  ---     ---  ---        

 

 -    ---     ---    ---    ----    

 ------  ---  ---  









------ '   ---  '   --- '   --- '        

                                    '  (  '  (  ' ( ' (

             

             '   ''       







   -  ---------------  ---------------------- -------------------------------------------------- ---   â&#x20AC;&#x201C;      +  

 â&#x20AC;&#x201C; 



 



â&#x20AC;&#x201C;         â&#x20AC;&#x201C;      +   ------------------------  ----------------------------------------------------  -------------------------  ------  ---  

 

 

  





     â&#x20AC;&#x201C;    â&#x20AC;&#x201C;      +   ------------------------  ----------------------------------------------------  -------------------------  ------  ---     â&#x20AC;&#x201C;      +  

 â&#x20AC;&#x201C; 





   





 â&#x20AC;&#x201C;      â&#x20AC;&#x201C;      +   -  ----------------------------------------------------  -------------------------   ----------------------â&#x20AC;&#x201C;

  â&#x20AC;&#x201C;      +  



 

                                   

                                         

   :       

      







 â&#x20AC;&#x201C;    

   â&#x20AC;&#x201C;      +   -  ----------------------------------------------------  ----------------------  ---  ----------------------  â&#x20AC;&#x201C; 

  â&#x20AC;&#x201C;      +  

  



   â&#x20AC;&#x201C;    â&#x20AC;&#x201C;      +   ------------------------  ----------------------------------------------------  -------------------------   

 â&#x20AC;&#x201C; 

  â&#x20AC;&#x201C;      +  

   

                                             



                    ' '   '  '              

             

                       

Â&#x2014; 188 Â&#x2014;

Â&#x2014; 189 Â&#x2014;


  ---     ---     ---    ---   



  ---     ---     ---  ---     ---  ---        

 

 -    ---     ---    ---    ----    

 ------  ---  ---  









------ '   ---  '   --- '   --- '        

                                    '  (  '  (  ' ( ' (

             

             '   ''       







   -  ---------------  ---------------------- -------------------------------------------------- ---   â&#x20AC;&#x201C;      +  

 â&#x20AC;&#x201C; 



 



â&#x20AC;&#x201C;         â&#x20AC;&#x201C;      +   ------------------------  ----------------------------------------------------  -------------------------  ------  ---  

 

 

  





     â&#x20AC;&#x201C;    â&#x20AC;&#x201C;      +   ------------------------  ----------------------------------------------------  -------------------------  ------  ---     â&#x20AC;&#x201C;      +  

 â&#x20AC;&#x201C; 





   





 â&#x20AC;&#x201C;      â&#x20AC;&#x201C;      +   -  ----------------------------------------------------  -------------------------   ----------------------â&#x20AC;&#x201C;

  â&#x20AC;&#x201C;      +  



 

                                   

                                         

   :       

      







 â&#x20AC;&#x201C;    

   â&#x20AC;&#x201C;      +   -  ----------------------------------------------------  ----------------------  ---  ----------------------  â&#x20AC;&#x201C; 

  â&#x20AC;&#x201C;      +  

  



   â&#x20AC;&#x201C;    â&#x20AC;&#x201C;      +   ------------------------  ----------------------------------------------------  -------------------------   

 â&#x20AC;&#x201C; 

  â&#x20AC;&#x201C;      +  

   

                                             



                    ' '   '  '              

             

                       

Â&#x2014; 188 Â&#x2014;

Â&#x2014; 189 Â&#x2014;


                           

       

       

 ---  

   ---    ---      

 ---   



 ---   

 ---   --- 



              

  04'$' =-:

    

    

        

 

  --- 

 



 



 ---

   

  --- 

  ---

  04'$'   =- :                     

     

        



    ---   --- 



             

   ---  

Â&#x2014; 190 Â&#x2014;

 --- 

 

                                               

          

         

 '  '      '   '                                               ''  ' '            

                  

    

    

 

                                                              1  1 1                  

Â&#x2014; 191 Â&#x2014;


                           

       

       

 ---  

   ---    ---      

 ---   



 ---   

 ---   --- 



              

  04'$' =-:

    

    

        

 

  --- 

 



 



 ---

   

  --- 

  ---

  04'$'   =- :                     

     

        



    ---   --- 



             

   ---  

Â&#x2014; 190 Â&#x2014;

 --- 

 

                                               

          

         

 '  '      '   '                                               ''  ' '            

                  

    

    

 

                                                              1  1 1                  

Â&#x2014; 191 Â&#x2014;


           

  1   

  

   

  

                                       11                         '  '' '' ' ' '' ''' ''                                                                                                                  

— 192 —

 ),%( 4' -$,"('  %  '     % F"-7('"# % ,"" 0   % P'$ -7 :%$' % %%#,#< ''                 %   --$,"('#'   %          

   ''  

 

           

 

 -   ---    ---   ---   ----  





           ;;                 ),%(%%$' "#$! '''-,( , #'   ---  # !#%%  %%   <

  -  F" -#'$-!-5   ---  ---     ---  ---- 

 -  ---  ---  ---  ----



   

 ,%9'-5 

35. Ðàçëîæåíèå íà ìíîæèòåëè ñóììû è ðàçíîñòè êóáîâ                         &&& &  

— 193 —




           

  1   

  

   

  

                                       11                         '  '' '' ' ' '' ''' ''                                                                                                                  

— 192 —

 ),%( 4' -$,"('  %  '     % F"-7('"# % ,"" 0   % P'$ -7 :%$' % %%#,#< ''                 %   --$,"('#'   %          

   ''  

 

           

 

 -   ---    ---   ---   ----  





           ;;                 ),%(%%$' "#$! '''-,( , #'   ---  # !#%%  %%   <

  -  F" -#'$-!-5   ---  ---     ---  ---- 

 -  ---  ---  ---  ----



   

 ,%9'-5 

35. Ðàçëîæåíèå íà ìíîæèòåëè ñóììû è ðàçíîñòè êóáîâ                         &&& &  

— 193 —




     '('(' '((                     

                                        ' ' ' '' 

 

           

  ---    ---  



  ---    ---      ---    ---   

    ---    ---  ---    ---     ---   --- 





   -   ---     ----  

     -    ---       ---    ---  ---    ----     

  -   ---     ---    ----

   









        



     -  ---------   ---    ---    ----        -  ------    ---  ---   ---  ---- 



                 

 --- '  --- '     --- '    --- ' --- ' 

     







                                                          0%$'       0%$'



 ---   ---     ---    ---   ---   



                   ' ''' '      

                   

Â&#x2014; 194 Â&#x2014;

           0%$' 







   



 0%$'      

 

 

 

  

   :     

Â&#x2014; 195 Â&#x2014;


     '('(' '((                     

                                        ' ' ' '' 

 

           

  ---    ---  



  ---    ---      ---    ---   

    ---    ---  ---    ---     ---   --- 





   -   ---     ----  

     -    ---       ---    ---  ---    ----     

  -   ---     ---    ----

   









        



     -  ---------   ---    ---    ----        -  ------    ---  ---   ---  ---- 



                 

 --- '  --- '     --- '    --- ' --- ' 

     







                                                          0%$'       0%$'



 ---   ---     ---    ---   ---   



                   ' ''' '      

                   

Â&#x2014; 194 Â&#x2014;

           0%$' 







   



 0%$'      

 

 

 

  

   :     

Â&#x2014; 195 Â&#x2014;


                                

  &#'%#'$#$%$9%#      

 &#'%#'$#$%$9%#          

         

        

§ 14. Ïðåîáðàçîâàíèå öåëûõ âûðàæåíèé 36. Ïðåîáðàçîâàíèå öåëîãî âûðàæåíèÿ â ìíîãî÷ëåí  _. 

 

–  --------------- 

 ---

                                                   

                                  

                

— 196 —

                                                                                           S                                                                 

                                                                             

                 

— 197 —


                                

  &#'%#'$#$%$9%#      

 &#'%#'$#$%$9%#          

         

        

§ 14. Ïðåîáðàçîâàíèå öåëûõ âûðàæåíèé 36. Ïðåîáðàçîâàíèå öåëîãî âûðàæåíèÿ â ìíîãî÷ëåí  _. 

 

–  --------------- 

 ---

                                                   

                                  

                

— 196 —

                                                                                           S                                                                 

                                                                             

                 

— 197 —


                    ---       ---   ---   





 ---      ---    ---  ---                                                           

      

 

   

 

             

                                                                   

    ---     ---   ---    ---  





 )       

  ---     ---      





 ---     

  

  

  )            

Â&#x2014; 198 Â&#x2014;

                                                                   F9%# #'                       F9%##'      0'#!9'

 ---  S     --- 



------        ---         



   --- 

  

     0'#!< 9'

     ---     ---     ---    

                                

             S     ),%(%%$' "'-,(%'2! <

- ''.5-,(0 ------  P'$ ''.5 ' ----



-,(! '' (4%%#,#''



 --------  --------   

   

 %%$'#' 

Â&#x2014; 199 Â&#x2014;


                    ---       ---   ---   





 ---      ---    ---  ---                                                           

      

 

   

 

             

                                                                   

    ---     ---   ---    ---  





 )       

  ---     ---      





 ---     

  

  

  )            

Â&#x2014; 198 Â&#x2014;

                                                                   F9%# #'                       F9%##'      0'#!9'

 ---  S     --- 



------        ---         



   --- 

  

     0'#!< 9'

     ---     ---     ---    

                                

             S     ),%(%%$' "'-,(%'2! <

- ''.5-,(0 ------  P'$ ''.5 ' ----



-,(! '' (4%%#,#''



 --------  --------   

   

 %%$'#' 

Â&#x2014; 199 Â&#x2014;


 ' ---  ' --- 

),%( %%( %#$!'" ! % # "   @   ' 0  @ &%%$'9,%"   --- 

F"   ---   --- 

   ---  ---  --- 

   --------  --------  --- 

  -  ---    ----

 %#$!'54%%%(:@

37. Ïðèìåíåíèå ðàçëè÷íûõ ñïîñîáîâ äëÿ ðàçëîæåíèÿ íà ìíîæèòåëè                               '   '  ''              

               

                                                                                              

— 200 —

            '' ' ' ' '                                                      '  (  '(' '(( ' (                

                         

               

                 

                                                                                                 

— 201 —


 ' ---  ' --- 

),%( %%( %#$!'" ! % # "   @   ' 0  @ &%%$'9,%"   --- 

F"   ---   --- 

   ---  ---  --- 

   --------  --------  --- 

  -  ---    ----

 %#$!'54%%%(:@

37. Ïðèìåíåíèå ðàçëè÷íûõ ñïîñîáîâ äëÿ ðàçëîæåíèÿ íà ìíîæèòåëè                               '   '  ''              

               

                                                                                              

— 200 —

            '' ' ' ' '                                                      '  (  '(' '(( ' (                

                         

               

                 

                                                                                                 

— 201 —


                                                                                        '    '    '   ' '                             '    '   ''                                                 ' ' ' ' '''''

Â&#x2014; 202 Â&#x2014;

                                                                            

    

   

    

      

       

                  

          

 = -:.6      

                 ),  -!#' 6 -%#('.6 % ' '    ! #,6 -%#('.6 % ' $!(' '  ! 6 0 ' $!(' %$'

Â&#x2014; 203 Â&#x2014;


                                                                                        '    '    '   ' '                             '    '   ''                                                 ' ' ' ' '''''

Â&#x2014; 202 Â&#x2014;

                                                                            

    

   

    

      

       

                  

          

 = -:.6      

                 ),  -!#' 6 -%#('.6 % ' '    ! #,6 -%#('.6 % ' $!(' '  ! 6 0 ' $!(' %$'

Â&#x2014; 203 Â&#x2014;


 ),%( %#'.               0%$'                    )                     )              =                F %  -'9"I, "                F "'-'9"I, #               F #-'9"I,

y

5

x

— 204 —

1 1 0 2

1 0 1

x

1 0 1

5 x –9

             >             =     =      0''$%,'%$'  -'' #%                       V %'%$' -'' #%

4 1 0 1

y

y

         =        =        =   !      !      !  =

  

y

 



38. Ïðèìåíåíèå ïðåîáðàçîâàíèé öåëûõ âûðàæåíèé

                 G'. -% '$"I% %(:'0 %%(:%2%%0    



-   -----

x

                 P' ' -, ''" #.9'$ ' %$ '   -''#%

— 205 —


 ),%( %#'.               0%$'                    )                     )              =                F %  -'9"I, "                F "'-'9"I, #               F #-'9"I,

y

5

x

— 204 —

1 1 0 2

1 0 1

x

1 0 1

5 x –9

             >             =     =      0''$%,'%$'  -'' #%                       V %'%$' -'' #%

4 1 0 1

y

y

         =        =        =   !      !      !  =

  

y

 



38. Ïðèìåíåíèå ïðåîáðàçîâàíèé öåëûõ âûðàæåíèé

                 G'. -% '$"I% %(:'0 %%(:%2%%0    



-   -----

x

                 P' ' -, ''" #.9'$ ' %$ '   -''#%

— 205 —


     - ---  ---  

 ---  ---      ---    ---   ---   ---  --- 









    - --- 

 ---  

 ---  ---   ---    ---   





       -  ---  ------  ------  ------  ---   --------  ------













        ;'  

;'    --- 



   -----

 -  ---   ---- 

-    ---  ---  ----



 ;'-(!#(%$#.#.9'         

                      

    

   

    

    $             

       

   `,.:#  %#(''. '5'.I,'2   WII,'25-%:%$ 

   

                0'. -% '$

— 206 —

 

        

y = –x + 6

y

y = x2

A

B 1

 

  

0 1 –2

x

= > 0 -% '$    ;     ;  ;  ;                                       

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå V Ê ïàðàãðàôó 12

   ---    ---    

------      ---    



    ---      --- 



    ---  

  --- 

— 207 —


     - ---  ---  

 ---  ---      ---    ---   ---   ---  --- 









    - --- 

 ---  

 ---  ---   ---    ---   





       -  ---  ------  ------  ------  ---   --------  ------













        ;'  

;'    --- 



   -----

 -  ---   ---- 

-    ---  ---  ----



 ;'-(!#(%$#.#.9'         

                      

    

   

    

    $             

       

   `,.:#  %#(''. '5'.I,'2   WII,'25-%:%$ 

   

                0'. -% '$

— 206 —

 

        

y = –x + 6

y

y = x2

A

B 1

 

  

0 1 –2

x

= > 0 -% '$    ;     ;  ;  ;                                       

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå V Ê ïàðàãðàôó 12

   ---    ---    

------      ---    



    ---      --- 



    ---  

  --- 

— 207 —


    

 

       

     

    

  

      

      



   

 

       

  

 

 

     

      



    

       



  

       

 

 

     

  :

  



 -    ---     ---  ---    ----





 '('( '(  '( ' (

 

-    ---  ------    ---  ---     ----





                                

        

-    ---   ---    ---   ---   ----

     

    -  ---   ------    ---  ---    ----









          

  ---  ---    ---   



        

-   ----    ---  

     





        

     ;                   

Ê ïàðàãðàôó 13      

       

   

     

  

  

 

  

      

   

     

           

          

    

 

— 208 —

— 209 —


    

 

       

     

    

  

      

      



   

 

       

  

 

 

     

      



    

       



  

       

 

 

     

  :

  



 -    ---     ---  ---    ----





 '('( '(  '( ' (

 

-    ---  ------    ---  ---     ----





                                

        

-    ---   ---    ---   ---   ----

     

    -  ---   ------    ---  ---    ----









          

  ---  ---    ---   



        

-   ----    ---  

     





        

     ;                   

Ê ïàðàãðàôó 13      

       

   

     

  

  

 

  

      

   

     

           

          

    

 

— 208 —

— 209 —


  

     

      

  

      

  ---  ---    ---     ---     ---  











 

- 

------  ----





---  ---    ---     ---  

------  ----







         

    

  



                                                                        ------   ---       ---     ---     ---     ---    

 



 â&#x20AC;&#x201C; +  -  ------  --------------------- 



                             

Â&#x2014; 210 Â&#x2014;

                                           

                                                                   ,#''7%$#9%#  -#%6                                                ' (' (' (' ( ' ( ' ' (        

  

       

                  

           

Â&#x2014; 211 Â&#x2014;


  

     

      

  

      

  ---  ---    ---     ---     ---  











 

- 

------  ----





---  ---    ---     ---  

------  ----







         

    

  



                                                                        ------   ---       ---     ---     ---     ---    

 



 â&#x20AC;&#x201C; +  -  ------  --------------------- 



                             

Â&#x2014; 210 Â&#x2014;

                                           

                                                                   ,#''7%$#9%#  -#%6                                                ' (' (' (' ( ' ( ' ' (        

  

       

                  

           

Â&#x2014; 211 Â&#x2014;


          

       

                

 

    

   

                                                        '  ' ' '' ' ''

                  

        

                 

       

 ---   ---   ---   ---    ---  ---   ---  ---   



  -  ------  ------   ---  ---   ---  --- 

 ---  ----  

           

   

    

    























                  

â&#x20AC;&#x201C;       â&#x20AC;&#x201C;      +   ------------------------  ----------------------------------------------------  ----------------------  ------   

   â&#x20AC;&#x201C;      +    â&#x20AC;&#x201C; 

 





      â&#x20AC;&#x201C;     â&#x20AC;&#x201C;       +   -  -----------------------------------------------------------------------  ----------------------  ---  --------------------------------  â&#x20AC;&#x201C; 

  â&#x20AC;&#x201C;      +  



 







 

   â&#x20AC;&#x201C;     â&#x20AC;&#x201C;      +   -  -------------------------------------------------------------------------  -------------------------------  ------  --------------------------------  â&#x20AC;&#x201C; 

  â&#x20AC;&#x201C;       

               

           '( ' (  ' (      

 



      ------   ---  ---   ---  --- 

 ---  

   

Â&#x2014; 212 Â&#x2014;



                                                                                                      

Â&#x2014; 213 Â&#x2014;


          

       

                

 

    

   

                                                        '  ' ' '' ' ''

                  

        

                 

       

 ---   ---   ---   ---    ---  ---   ---  ---   



  -  ------  ------   ---  ---   ---  --- 

 ---  ----  

           

   

    

    























                  

â&#x20AC;&#x201C;       â&#x20AC;&#x201C;      +   ------------------------  ----------------------------------------------------  ----------------------  ------   

   â&#x20AC;&#x201C;      +    â&#x20AC;&#x201C; 

 





      â&#x20AC;&#x201C;     â&#x20AC;&#x201C;       +   -  -----------------------------------------------------------------------  ----------------------  ---  --------------------------------  â&#x20AC;&#x201C; 

  â&#x20AC;&#x201C;      +  



 







 

   â&#x20AC;&#x201C;     â&#x20AC;&#x201C;      +   -  -------------------------------------------------------------------------  -------------------------------  ------  --------------------------------  â&#x20AC;&#x201C; 

  â&#x20AC;&#x201C;       

               

           '( ' (  ' (      

 



      ------   ---  ---   ---  --- 

 ---  

   

Â&#x2014; 212 Â&#x2014;



                                                                                                      

Â&#x2014; 213 Â&#x2014;


            )                       3 3         )              

          

       ' '  ''  

  

------     ---     ---     ------  ---           













   -    ---   ---       ----   

    ---     ---  ---  



------     ---    

  ---      ---  ---      ------    ---------     

           0< %$'                                                                             

                                                         





------   ---        ---      

          





           0%$'                0%$'        0%$'

— 214 —

Ê ïàðàãðàôó 14                                           

— 215 —


            )                       3 3         )              

          

       ' '  ''  

  

------     ---     ---     ------  ---           













   -    ---   ---       ----   

    ---     ---  ---  



------     ---    

  ---      ---  ---      ------    ---------     

           0< %$'                                                                             

                                                         





------   ---        ---      

          





           0%$'                0%$'        0%$'

— 214 —

Ê ïàðàãðàôó 14                                           

— 215 —




     

       

               



                               

        





          

 

    

 



   ---

                                   





    

     

       `,'2$#    '5'$ %         F %-'9"I, "         F "'-'9"I, 

             )               

                           

            

  

                 

      



      

     

                              

)!,#,: %(#'%#                                                         ), -#,: %(#'%# )!,#,: %(#'%#             

             

        

         )    

      ), -#,: %(#'%#

Â&#x2014; 216 Â&#x2014;

Â&#x2014; 217 Â&#x2014;




     

       

               



                               

        





          

 

    

 



   ---

                                   





    

     

       `,'2$#    '5'$ %         F %-'9"I, "         F "'-'9"I, 

             )               

                           

            

  

                 

      



      

     

                              

)!,#,: %(#'%#                                                         ), -#,: %(#'%# )!,#,: %(#'%#             

             

        

         )    

      ), -#,: %(#'%#

Â&#x2014; 216 Â&#x2014;

Â&#x2014; 217 Â&#x2014;


 ''  ''''  '''  ''''' )'          

      ---    

     ---      

       ---     



)!,#,: %(#'%#             )!,-#,: %(#'%#                              



)!,#,: %(#'%# ' ( 2 + ' 2 ( 2 ' +  ( + )!,-#,: %(#'%# '2(+ '+(2  ' 2  '2(+ ( + ' +  '+(2? 2  ' 2  ( + ' + ( 2 ' ( 2 + 



             )-, '" ''%9 )-, '" ''%9



                D'" ''%9 -   G1II2'.-  #'.%    



                                  

                  

    ---   ---    ---   --- 

      

                       



 

                                                                                                               )                )                    

  

 )   

Â&#x2014; 218 Â&#x2014;

Â&#x2014; 219 Â&#x2014;


 ''  ''''  '''  ''''' )'          

      ---    

     ---      

       ---     



)!,#,: %(#'%#             )!,-#,: %(#'%#                              



)!,#,: %(#'%# ' ( 2 + ' 2 ( 2 ' +  ( + )!,-#,: %(#'%# '2(+ '+(2  ' 2  '2(+ ( + ' +  '+(2? 2  ' 2  ( + ' + ( 2 ' ( 2 + 



             )-, '" ''%9 )-, '" ''%9



                D'" ''%9 -   G1II2'.-  #'.%    



                                  

                  

    ---   ---    ---   --- 

      

                       



 

                                                                                                               )                )                    

  

 )   

Â&#x2014; 218 Â&#x2014;

Â&#x2014; 219 Â&#x2014;


    

 

 

       

                    

            ---

    

      

     -      ------      ---     ---    ----



 

 



  

 

 =-#%6 1'%#'' 4'

    ---      ---  ------         ---         









     



   

                                  



   



   

    

                

Â&#x2014; 220 Â&#x2014;

    

                

                            

                                                           ' ' '  '  '             

   ---

   

  

                            ---

   

  

      

   --- 



                                          '  '''' ''

Â&#x2014; 221 Â&#x2014;


    

 

 

       

                    

            ---

    

      

     -      ------      ---     ---    ----



 

 



  

 

 =-#%6 1'%#'' 4'

    ---      ---  ------         ---         









     



   

                                  



   



   

    

                

Â&#x2014; 220 Â&#x2014;

    

                

                            

                                                           ' ' '  '  '             

   ---

   

  

                            ---

   

  

      

   --- 



                                          '  '''' ''

Â&#x2014; 221 Â&#x2014;


     

                  

             



                    

                                       



      

             

                     

  

            

                

           

' '  '' '' '' ' '''' '

                                                   

                           

                     

        

       

             

          

          

                      

  

             

            

          

   

       

              



        

      

      

  

     

Â&#x2014; 222 Â&#x2014;

Â&#x2014; 223 Â&#x2014;


     

                  

             



                    

                                       



      

             

                     

  

            

                

           

' '  '' '' '' ' '''' '

                                                   

                           

                     

        

       

             

          

          

                      

  

             

            

          

   

       

              



        

      

      

  

     

Â&#x2014; 222 Â&#x2014;

Â&#x2014; 223 Â&#x2014;


à ë à â à VI

             

ÑÈÑÒÅÌÛ ËÈÍÅÉÍÛÕ ÓÐÀÂÍÅÍÈÉ

                               

   '9        '9

§ 15. Ëèíåéíûå óðàâíåíèÿ ñ äâóìÿ ïåðåìåííûìè è èõ ñèñòåìû

         9- #.9'#'   9- #.9< '#'  9-#.< 9'#' 

      

39. Ëèíåéíîå óðàâíåíèå ñ äâóìÿ ïåðåìåííûìè 

N ? N ?



N ? N N



      ---    ---    0 %#('    ---  

                                 0'%$' -#%"< %$' #'%$ 

         #%( *.#!#%## %' #:7%$'  ',9' %#-%'::2I, ,'9(%#4%$ %'%,:7!'',(' % !,(,--%(%-#                    

— 224 —







 --- 04',#''$        

                                           



      



    '       '   

$#$%$ $#$%$  $#$%$   '$#$%$

— 225 —


à ë à â à VI

             

ÑÈÑÒÅÌÛ ËÈÍÅÉÍÛÕ ÓÐÀÂÍÅÍÈÉ

                               

   '9        '9

§ 15. Ëèíåéíûå óðàâíåíèÿ ñ äâóìÿ ïåðåìåííûìè è èõ ñèñòåìû

         9- #.9'#'   9- #.9< '#'  9-#.< 9'#' 

      

39. Ëèíåéíîå óðàâíåíèå ñ äâóìÿ ïåðåìåííûìè 

N ? N ?



N ? N N



      ---    ---    0 %#('    ---  

                                 0'%$' -#%"< %$' #'%$ 

         #%( *.#!#%## %' #:7%$'  ',9' %#-%'::2I, ,'9(%#4%$ %'%,:7!'',(' % !,(,--%(%-#                    

— 224 —







 --- 04',#''$        

                                           



      



    '       '   

$#$%$ $#$%$  $#$%$   '$#$%$

— 225 —


   

     '

   3

  

            

                          

   

 --- 

 

 ---  

40. Ãðàôèê ëèíåéíîãî óðàâíåíèÿ ñ äâóìÿ ïåðåìåííûìè

  @, , @  @, @, @ --- ,

 % " #  $

                              

            

               

             

             

 

 



     

             1

             %            

   

                   );          )      

— 226 —

 % "  #  $

 '  '   '  

         

-'9 -'9 -'9 '-'9

 6                         



 

y

 

å) 4

      



 

  

 

–4

 ---

 

— 227 —



à) 4 x á)

ä)   

â) 1 0 1

ã)


   

     '

   3

  

            

                          

   

 --- 

 

 ---  

40. Ãðàôèê ëèíåéíîãî óðàâíåíèÿ ñ äâóìÿ ïåðåìåííûìè

  @, , @  @, @, @ --- ,

 % " #  $

                              

            

               

             

             

 

 



     

             1

             %            

   

                   );          )      

— 226 —

 % "  #  $

 '  '   '  

         

-'9 -'9 -'9 '-'9

 6                         



 

y

 

å) 4

      



 

  

 

–4

 ---

 

— 227 —



à) 4 x á)

ä)   

â) 1 0 1

ã)


  

   



$ 

$  $   $  

    

$  $$

             





y â)

à )

 â&#x20AC;&#x201C;

 â&#x20AC;&#x201C;

-  ---------------  $   --------------

ã)

 



1 0 1

   

 

$ $  )*****+     H333      H33Z

x

     $  $ $  +  â&#x20AC;&#x201C;  -  ----------------   -------------

á)

              

       

              

 



á)

         

Â&#x2014; 228 Â&#x2014;



           

x â)

  



    

1 1 0



    



à )

ã)

    



) ---     ---    ---  

y

 



  -   ------  ------  ---  ) ----







 ---  ---  

41. Ã&#x2018;èñòåìû ëèíåéíûõ óðà âíåíèé ñ äâóìÿ ïåðåìåííûìè   



 ?$#$%$ 

  

3 

  E#$%$   

Â&#x2014; 229 Â&#x2014;


  

   



$ 

$  $   $  

    

$  $$

             





y â)

à )

 â&#x20AC;&#x201C;

 â&#x20AC;&#x201C;

-  ---------------  $   --------------

ã)

 



1 0 1

   

 

$ $  )*****+     H333      H33Z

x

     $  $ $  +  â&#x20AC;&#x201C;  -  ----------------   -------------

á)

              

       

              

 



á)

         

Â&#x2014; 228 Â&#x2014;



           

x â)

  



    

1 1 0



    



à )

ã)

    



) ---     ---    ---  

y

 



  -   ------  ------  ---  ) ----







 ---  ---  

41. Ã&#x2018;èñòåìû ëèíåéíûõ óðà âíåíèé ñ äâóìÿ ïåðåìåííûìè   



 ?$#$%$ 

  

3 

  E#$%$   

Â&#x2014; 229 Â&#x2014;


 --- 





A(â&#x20AC;&#x201C;2; 2)



y 1 y = â&#x20AC;&#x201C;â&#x20AC;&#x201C;x + 3 3 A(3; 2) 1 0 1 y=xâ&#x20AC;&#x201C;1

6 2 0 â&#x20AC;&#x201C;2

 --- 

 

Â&#x2014; 230 Â&#x2014;

10

   ---



y=3 â&#x20AC;&#x201C;x + 31 â&#x20AC;&#x201C; 4 2

              

      

6 10 14 18 22 16 20 x y = â&#x20AC;&#x201C;x â&#x20AC;&#x201C;4 2



x

 

Â&#x2014; 231 Â&#x2014;

y 3

   ---

  

â&#x20AC;&#x201C;

 

x



y 20 18 16 14

1,2

 

 --- 





 

x

 

       ---  ---      

 ---  ---  

D(0; 2)

â&#x20AC;&#x201C;

 



,3 x

 

1 1 0 y=2 â&#x20AC;&#x201C;x + 2 5

 

             



â&#x20AC;&#x201C;0

   

  



y=

    

 



y 1 y = â&#x20AC;&#x201C;â&#x20AC;&#x201C;x + 2 2

1,5

       ?$#$%$      ?$#$%$     E#$%$           ?$#$%$      E#$%$     ?$#$%$  

 

 --- 

=



 ---         --- 

    

10 1

y

 @, @,     E#$%$ @ ,     , @     E#$%$  @ ,  

x

A(1; â&#x20AC;&#x201C;1,5)


 --- 





A(â&#x20AC;&#x201C;2; 2)



y 1 y = â&#x20AC;&#x201C;â&#x20AC;&#x201C;x + 3 3 A(3; 2) 1 0 1 y=xâ&#x20AC;&#x201C;1

6 2 0 â&#x20AC;&#x201C;2

 --- 

 

Â&#x2014; 230 Â&#x2014;

10

   ---



y=3 â&#x20AC;&#x201C;x + 31 â&#x20AC;&#x201C; 4 2

              

      

6 10 14 18 22 16 20 x y = â&#x20AC;&#x201C;x â&#x20AC;&#x201C;4 2



x

 

Â&#x2014; 231 Â&#x2014;

y 3

   ---

  

â&#x20AC;&#x201C;

 

x



y 20 18 16 14

1,2

 

 --- 





 

x

 

       ---  ---      

 ---  ---  

D(0; 2)

â&#x20AC;&#x201C;

 



,3 x

 

1 1 0 y=2 â&#x20AC;&#x201C;x + 2 5

 

             



â&#x20AC;&#x201C;0

   

  



y=

    

 



y 1 y = â&#x20AC;&#x201C;â&#x20AC;&#x201C;x + 2 2

1,5

       ?$#$%$      ?$#$%$     E#$%$           ?$#$%$      E#$%$     ?$#$%$  

 

 --- 

=



 ---         --- 

    

10 1

y

 @, @,     E#$%$ @ ,     , @     E#$%$  @ ,  

x

A(1; â&#x20AC;&#x201C;1,5)


   

   --- 



    

 --- 

 --- 

 





 --- 

y

 

1 0 1

y=1 â&#x20AC;&#x201C;x â&#x20AC;&#x201C; 3 2 x

A(0; â&#x20AC;&#x201C;3)

 

y = â&#x20AC;&#x201C;3 â&#x20AC;&#x201C;x â&#x20AC;&#x201C; 3 2





 

 

 ---  ---  

  

0



    

x

;â&#x20AC;&#x201C; 1) A( â&#x20AC;&#x201C;1

 ---                    ---   

        ---  

L'4'

    

      



 ---  ---  





 -  ---  -----

  L'4'  

        

        

  --- 

  

  ---         

     

  ---        

 

 

+ â&#x20AC;&#x201C; ----------------   ------------   



â&#x20AC;&#x201C;  

+   ----------------   ------------  

        -         -----

Â&#x2014; 233 Â&#x2014;



  ---

L%' ''"4'5



Â&#x2014; 232 Â&#x2014;



L'4'   

 

y = â&#x20AC;&#x201C;2 â&#x20AC;&#x201C;x â&#x20AC;&#x201C; 5 â&#x20AC;&#x201C; 3 3

L'4'  

1

 ---           

      ---  ---

 

y=x

1



 



y

L'4'

             ?4'5              L%' ''9%#4'5

L'4'

 

       ---  ---        

 ---                 --- 




   

   --- 



    

 --- 

 --- 

 





 --- 

y

 

1 0 1

y=1 â&#x20AC;&#x201C;x â&#x20AC;&#x201C; 3 2 x

A(0; â&#x20AC;&#x201C;3)

 

y = â&#x20AC;&#x201C;3 â&#x20AC;&#x201C;x â&#x20AC;&#x201C; 3 2





 

 

 ---  ---  

  

0



    

x

;â&#x20AC;&#x201C; 1) A( â&#x20AC;&#x201C;1

 ---                    ---   

        ---  

L'4'

    

      



 ---  ---  





 -  ---  -----

  L'4'  

        

        

  --- 

  

  ---         

     

  ---        

 

 

+ â&#x20AC;&#x201C; ----------------   ------------   



â&#x20AC;&#x201C;  

+   ----------------   ------------  

        -         -----

Â&#x2014; 233 Â&#x2014;



  ---

L%' ''"4'5



Â&#x2014; 232 Â&#x2014;



L'4'   

 

y = â&#x20AC;&#x201C;2 â&#x20AC;&#x201C;x â&#x20AC;&#x201C; 5 â&#x20AC;&#x201C; 3 3

L'4'  

1

 ---           

      ---  ---

 

y=x

1



 



y

L'4'

             ?4'5              L%' ''9%#4'5

L'4'

 

       ---  ---        

 ---                 --- 








 – 

– ----------------  ---    ---------------------  --------       



    

 ------   ------

 



                                                                     

§ 16. Ðåøåíèå ñèñòåì ëèíåéíûõ óðàâíåíèé 42. Ñïîñîá ïîäñòàíîâêè  

   

     

       ---  

 

 ---  

 ---  

 ---  

   ---  ---  



                   

  

    



  

  

  

  

                     

  

 



 

 

                 

                      

 

                   

        

 

     

                      

  

 

                                                

  

   



                       

          

 



 

 

— 234 —

                     

                      

 

                             



       



— 235 —






 – 

– ----------------  ---    ---------------------  --------       



    

 ------   ------

 



                                                                     

§ 16. Ðåøåíèå ñèñòåì ëèíåéíûõ óðàâíåíèé 42. Ñïîñîá ïîäñòàíîâêè  

   

     

       ---  

 

 ---  

 ---  

 ---  

   ---  ---  



                   

  

    



  

  

  

  

                     

  

 



 

 

                 

                      

 

                   

        

 

     

                      

  

 

                                                

  

   



                       

          

 



 

 

— 234 —

                     

                      

 

                             



       



— 235 —




------   , ,  , , , 

 

            

       

   

 

  

    

  



            

'(  '  (

 

       

 



@ , @ ,     @ ,  @ ,

@ --- 

, ---



@ --- ,

, ,

, --- 

' ---  

 --- (( 

(  '

 â&#x20AC;&#x201C; , - ,   ------------------

 --- (( 



 â&#x20AC;&#x201C; , - @ -----------------

@, 

 ---  



 ---           

  

    ---  

    

    

 

      --- 



         ---  ------     

  

  

  

------          

   ---     



 ------   ---   

 â&#x20AC;&#x201C;  , ---------------------- ,  

Â&#x2014; 236 Â&#x2014;





 

 ---    



 --- 

' --- (

--- (  ( 

@, @,  @,  @,  

   ---  ---   

--- (( 



@ --- ,

'( '(  '(  '( 

( 



   

 ---           ---    

    

 ---  

     --- ,   ,

'(  '(   ' (  '  (

(  (   '    ' 

  

@ --- ,

, --- 

   ---  --- 

 @ --- 

  ((   (  ( 

                 

, --- 

 â&#x20AC;&#x201C; , -------------------  @  



   



                                  



Â&#x2014; 237 Â&#x2014;




------   , ,  , , , 

 

            

       

   

 

  

    

  



            

'(  '  (

 

       

 



@ , @ ,     @ ,  @ ,

@ --- 

, ---



@ --- ,

, ,

, --- 

' ---  

 --- (( 

(  '

 â&#x20AC;&#x201C; , - ,   ------------------

 --- (( 



 â&#x20AC;&#x201C; , - @ -----------------

@, 

 ---  



 ---           

  

    ---  

    

    

 

      --- 



         ---  ------     

  

  

  

------          

   ---     



 ------   ---   

 â&#x20AC;&#x201C;  , ---------------------- ,  

Â&#x2014; 236 Â&#x2014;





 

 ---    



 --- 

' --- (

--- (  ( 

@, @,  @,  @,  

   ---  ---   

--- (( 



@ --- ,

'( '(  '(  '( 

( 



   

 ---           ---    

    

 ---  

     --- ,   ,

'(  '(   ' (  '  (

(  (   '    ' 

  

@ --- ,

, --- 

   ---  --- 

 @ --- 

  ((   (  ( 

                 

, --- 

 â&#x20AC;&#x201C; , -------------------  @  



   



                                  



Â&#x2014; 237 Â&#x2014;


 

           ---  ------     

  

  

  

------ 

 ---   



  ------  ---------        ------    

  ---    



        --- 

------ 

 ---     ------    ---  ---       --- 

 ------   ------ 

 ---   







   ---   ---  







------  ------  



 ------  ---   

   







 ------  ---    



  









 ---  --- 









 

 



  ---  ------   



 ---  ---   ---  --- 





 



    

 

       --- 

  

Â&#x2014; 238 Â&#x2014;

 ---





                         



    ---      --- 

 --- 

 ---

                   



                  

 --- 

     ---  



         --- 

    ---  ---     

 ---    --- 

 --- 



+  -   --------------+ ----------------  



    

+     -    --------------  



 ---  

 --- 

 --- 

 



      ---   ---    ------ 

  

          ---  ---  



           

  

   ------  ---   

                          



     



                        

 

 --- 

  â&#x20AC;&#x201C;  --- +     ----------------------

 ---  



   ---     

                          

                

  

Â&#x2014; 239 Â&#x2014;


 

           ---  ------     

  

  

  

------ 

 ---   



  ------  ---------        ------    

  ---    



        --- 

------ 

 ---     ------    ---  ---       --- 

 ------   ------ 

 ---   







   ---   ---  







------  ------  



 ------  ---   

   







 ------  ---    



  









 ---  --- 









 

 



  ---  ------   



 ---  ---   ---  --- 





 



    

 

       --- 

  

Â&#x2014; 238 Â&#x2014;

 ---





                         



    ---      --- 

 --- 

 ---

                   



                  

 --- 

     ---  



         --- 

    ---  ---     

 ---    --- 

 --- 



+  -   --------------+ ----------------  



    

+     -    --------------  



 ---  

 --- 

 --- 

 



      ---   ---    ------ 

  

          ---  ---  



           

  

   ------  ---   

                          



     



                        

 

 --- 

  â&#x20AC;&#x201C;  --- +     ----------------------

 ---  



   ---     

                          

                

  

Â&#x2014; 239 Â&#x2014;


               

                          

                --- 

 

 

 --- 

 --- 

 --- 

     ---  ---   



     

    

        

       

                      

                                 

 

---  ---  

---  ---  



--------  --------   

 --------  ---   

     

       

     

  

Â&#x2014; 240 Â&#x2014;

 ---      ---  

                       

 





 ---      --- 

  --------  ---      ------  ------   

    -------------  --------       ----------  ------------   

â&#x20AC;&#x201C;  -------------------             â&#x20AC;&#x201C;   -------------------    

        â&#x20AC;&#x201C;   â&#x20AC;&#x201C;  -------------------------------    



------     

 ------ 

       



    ------      

------  

 

 +   ---------------------  +  ----------------------     



      

   

 

---  ---   

------  ------   

+ 

----------------------    

  

  --------  --------     

 --------  --------   

     

+ 

---------------------         

   

 



Â&#x2014; 241 Â&#x2014;

  


               

                          

                --- 

 

 

 --- 

 --- 

 --- 

     ---  ---   



     

    

        

       

                      

                                 

 

---  ---  

---  ---  



--------  --------   

 --------  ---   

     

       

     

  

Â&#x2014; 240 Â&#x2014;

 ---      ---  

                       

 





 ---      --- 

  --------  ---      ------  ------   

    -------------  --------       ----------  ------------   

â&#x20AC;&#x201C;  -------------------             â&#x20AC;&#x201C;   -------------------    

        â&#x20AC;&#x201C;   â&#x20AC;&#x201C;  -------------------------------    



------     

 ------ 

       



    ------      

------  

 

 +   ---------------------  +  ----------------------     



      

   

 

---  ---   

------  ------   

+ 

----------------------    

  

  --------  --------     

 --------  --------   

     

+ 

---------------------         

   

 



Â&#x2014; 241 Â&#x2014;

  






------  ------    

------  ------    

   ------------  ------    

   --------  --------------    

  ---    ---   ---     ---  



    

     

             

   

 

  

                   -------  ------        ---  ---          ------  





  ---  ---  ---    ---  ---  ---

----------   ------     

   ---   ---       ------    





 ----------  ------ 

   ---  ---  ------  ------ 









                                                            ---  ---   ---  ---  ---  ---  

  





Â&#x2014; 242 Â&#x2014;

            =-:!' ' 

43. Ã&#x2018;ïîñîá ñëîæåíèÿ      

             

    

         

 

 

    



                        

                  

 

           

 

 

       ---

    ---   

   

         

 

        

 



 ---      ---        ---  



  ---  ---  ---     ---  ---  

  ---    ---       ---  

  



  ---       ---      ---    ---      ---     

   





                         

  ---     ---    ---    ---     ---   



Â&#x2014; 243 Â&#x2014;






------  ------    

------  ------    

   ------------  ------    

   --------  --------------    

  ---    ---   ---     ---  



    

     

             

   

 

  

                   -------  ------        ---  ---          ------  





  ---  ---  ---    ---  ---  ---

----------   ------     

   ---   ---       ------    





 ----------  ------ 

   ---  ---  ------  ------ 









                                                            ---  ---   ---  ---  ---  ---  

  





Â&#x2014; 242 Â&#x2014;

            =-:!' ' 

43. Ã&#x2018;ïîñîá ñëîæåíèÿ      

             

    

         

 

 

    



                        

                  

 

           

 

 

       ---

    ---   

   

         

 

        

 



 ---      ---        ---  



  ---  ---  ---     ---  ---  

  ---    ---       ---  

  



  ---       ---      ---    ---      ---     

   





                         

  ---     ---    ---    ---     ---   



Â&#x2014; 243 Â&#x2014;




                   





       

               

 

        

   

  

 



    

   

  

 

 

 

                      



 ---  

 ---  



  ---   

                          

      

           

  ---   ---           ---  --- 

  --- 

   ---      



        

               



   

  

      



         

      



    

              

    

Â&#x2014; 244 Â&#x2014;

 --- 

 ---      ---  ---    

 ---     ---    

 !    !  

 !    ! 

  !  !  !     !

       !  

                

          

   

@ ,  @,  @,  @, 

@  @ @    , @,  ,                       

    

 

             



     

      

               



           

     

  



           

Â&#x2014; 245 Â&#x2014;




                   





       

               

 

        

   

  

 



    

   

  

 

 

 

                      



 ---  

 ---  



  ---   

                          

      

           

  ---   ---           ---  --- 

  --- 

   ---      



        

               



   

  

      



         

      



    

              

    

Â&#x2014; 244 Â&#x2014;

 --- 

 ---      ---  ---    

 ---     ---    

 !    !  

 !    ! 

  !  !  !     !

       !  

                

          

   

@ ,  @,  @,  @, 

@  @ @    , @,  ,                       

    

 

             



     

      

               



           

     

  



           

Â&#x2014; 245 Â&#x2014;


 @ ,   @,  @  ,   @,   ,   ,    @,  @   @  @    ,  ,                           

      





                        

                          

 5    8                            6  7                       %   "                          #   $         

               

Â&#x2014; 246 Â&#x2014;

      

           

  

  

% " 

             

 --- 

   ---   

 ---  

 --- 

  ---  ---







 F -% '$%%$'   

        

         WI-6 !    

        

    

                           

        

       

   

           

           

            

        

                  

 

       

Â&#x2014; 247 Â&#x2014;


 @ ,   @,  @  ,   @,   ,   ,    @,  @   @  @    ,  ,                           

      





                        

                          

 5    8                            6  7                       %   "                          #   $         

               

Â&#x2014; 246 Â&#x2014;

      

           

  

  

% " 

             

 --- 

   ---   

 ---  

 --- 

  ---  ---







 F -% '$%%$'   

        

         WI-6 !    

        

    

                           

        

       

   

           

           

            

        

                  

 

       

Â&#x2014; 247 Â&#x2014;


 

  ---  ---     

  --------  --------     

    

                    



   



  ---  ---   

  --------  --------   





 ---  ------      ---  ------   

 ---  

        

  --- @ --- ,  

---  ---     

  



-------  --------     

                    

 

               

  

  ---  ---  





       

 

 



Â&#x2014; 248 Â&#x2014;

     

     

  

  

 

------   ---    

------   ---   

  ------------  --------  

    

               

   

 ---  ------   ---  ------   

 @,  @ ,  @ @ ,   @ ,  @ ,  @,  @  @  ,   , 

 

        



  --- @ --------   



------  ---           



                   

      ---  ---- 

------  ---  



 

  ---  ------    

 

   

  --------  ------     

                        

 

          --- , --- a 





 

-------- , --------   

@ , 

, @  ,



,@    

,@  , @

,@ 

 

, , 

@  @    

---  ---   

  



      

   

  --------  --------    

      

    

   

Â&#x2014; 249 Â&#x2014;


 

  ---  ---     

  --------  --------     

    

                    



   



  ---  ---   

  --------  --------   





 ---  ------      ---  ------   

 ---  

        

  --- @ --- ,  

---  ---     

  



-------  --------     

                    

 

               

  

  ---  ---  





       

 

 



Â&#x2014; 248 Â&#x2014;

     

     

  

  

 

------   ---    

------   ---   

  ------------  --------  

    

               

   

 ---  ------   ---  ------   

 @,  @ ,  @ @ ,   @ ,  @ ,  @,  @  @  ,   , 

 

        



  --- @ --------   



------  ---           



                   

      ---  ---- 

------  ---  



 

  ---  ------    

 

   

  --------  ------     

                        

 

          --- , --- a 





 

-------- , --------   

@ , 

, @  ,



,@    

,@  , @

,@ 

 

, , 

@  @    

---  ---   

  



      

   

  --------  --------    

      

    

   

Â&#x2014; 249 Â&#x2014;




     ---  ---  ---   



 ),%( # I# #.-,7'  !5  # $'# 0  !'$ #I##.-,7'' !5(4%< %#,#''   P'$%(!5#.-,7'!#%$2%%# #,#''  

  





--------  --------  --------    



                        

       

    



   

          

            ---

?4'5               L%' ''9%#4'5



                                                     

     

                                %:'$ -"4'%( #'   %:'$-"4'%(   %:'$-"4'%(

44. Ðåøåíèå çàäà÷ ñ ïîìîùüþ ñèñòåì óðàâíåíèé

 #I# 0!5#$'#0  !5  ),%( ' "' -$ : " " ,"60  P'$ #%""%%#,#''   P'$  ' "' -$  '  " (4-, #,#''  

 

  



 

  

  ":'"'-$  ),%(",!#.6#5 "#.6 P'$ "< #.64'' '(4%%#,#''     !'$ #%" #$-, #,#''

 

  

  



  

  

  ",!#.6#5  ),%(!,- 4' # P'$  # !,- #   ! (4 %%< #,#'' 

F#%"!,- < #4'-, #,#''     R 

  

  



  



 

 

 ),%(' % # F"!'$6%,,%< %#',#''  !'$!'%( 0,< "  

   

 

  

      %  

 ),%(#$%' %'#' % P'$ %'#''%(4#5%'.%< %#,#''   

— 250 —

— 251 —

 4'#




     ---  ---  ---   



 ),%( # I# #.-,7'  !5  # $'# 0  !'$ #I##.-,7'' !5(4%< %#,#''   P'$%(!5#.-,7'!#%$2%%# #,#''  

  





--------  --------  --------    



                        

       

    



   

          

            ---

?4'5               L%' ''9%#4'5



                                                     

     

                                %:'$ -"4'%( #'   %:'$-"4'%(   %:'$-"4'%(

44. Ðåøåíèå çàäà÷ ñ ïîìîùüþ ñèñòåì óðàâíåíèé

 #I# 0!5#$'#0  !5  ),%( ' "' -$ : " " ,"60  P'$ #%""%%#,#''   P'$  ' "' -$  '  " (4-, #,#''  

 

  



 

  

  ":'"'-$  ),%(",!#.6#5 "#.6 P'$ "< #.64'' '(4%%#,#''     !'$ #%" #$-, #,#''

 

  

  



  

  

  ",!#.6#5  ),%(!,- 4' # P'$  # !,- #   ! (4 %%< #,#'' 

F#%"!,- < #4'-, #,#''     R 

  

  



  



 

 

 ),%(' % # F"!'$6%,,%< %#',#''  !'$!'%( 0,< "  

   

 

  

      %  

 ),%(#$%' %'#' % P'$ %'#''%(4#5%'.%< %#,#''   

— 250 —

— 251 —

 4'#


P'$--, #,#''               

      #$%'#' %  ),%( -'%( :'$  "@ -'%( 9! "@  P'$  -'%( :'$ '  "@ '(4%%#,#''    D%% :'$  "  9! 0   "  P'$  #%$%%#' "-, ,#''                                         

   -'%(:'$ "@  ),%( 0-9'$$,95'%(I$ '#$ ;95'%(,# %(' % "   + , % -7(:   " %:      % , % "%'(4  +%##,#''                         

 

      '(4%- %"-(0-   ),%(%%(4'. @ %%(-! @ P'$  %%( -! (4 %%# ,#''   ),('4'0 '-!0 #%"             

            

         %%(-!@

Â&#x2014; 252 Â&#x2014;

 ),%(-# %#' # F"      

                       

   

  %   ),%(  @  0 %%( -6 -  ':  @ 0 "%%(-# '$ ), ,#''$       

                                  

 

 %%(- ': @ -# '$0  @  ),%(%%(.%"#$  @   ''" @ F"            

        3 

  

 

  

     %%(-#"#$ @ #" 0 @  ),%(%%(-#",% @ #" 0 @ P'$#$-,(%%#,#''   F-#.5-4' (4#"#%< -, #,#''          

               

 

          %%( -#" ,%  @   #" 0  @

Â&#x2014; 253 Â&#x2014;


P'$--, #,#''               

      #$%'#' %  ),%( -'%( :'$  "@ -'%( 9! "@  P'$  -'%( :'$ '  "@ '(4%%#,#''    D%% :'$  "  9! 0   "  P'$  #%$%%#' "-, ,#''                                         

   -'%(:'$ "@  ),%( 0-9'$$,95'%(I$ '#$ ;95'%(,# %(' % "   + , % -7(:   " %:      % , % "%'(4  +%##,#''                         

 

      '(4%- %"-(0-   ),%(%%(4'. @ %%(-! @ P'$  %%( -! (4 %%# ,#''   ),('4'0 '-!0 #%"             

            

         %%(-!@

Â&#x2014; 252 Â&#x2014;

 ),%(-# %#' # F"      

                       

   

  %   ),%(  @  0 %%( -6 -  ':  @ 0 "%%(-# '$ ), ,#''$       

                                  

 

 %%(- ': @ -# '$0  @  ),%(%%(.%"#$  @   ''" @ F"            

        3 

  

 

  

     %%(-#"#$ @ #" 0 @  ),%(%%(-#",% @ #" 0 @ P'$#$-,(%%#,#''   F-#.5-4' (4#"#%< -, #,#''          

               

 

          %%( -#" ,%  @   #" 0  @

Â&#x2014; 253 Â&#x2014;


 ),%( @ 0%%(#%$ 5# @ 0 %%(  '$  F" -,  ,#''$                       

 

  

    

  

 



 %%(#%$ 5# @  ),%( %%#''$ %%( -6  @   %%(  '$ @ P'$ #$ -  ':  -# %%# ,#''       P'$#$-,(-# '$- ':-,  ,",#''                   

     

                            

 

       

&4%%,  ---  ---       ---  ---     

(4    ---    ---

       ---    --- 

 --- 



 ---  ---    

 

 

  %  ),%(  "@% 0 -'%( 9!  "@% 0 -'%(  ), ,#''$       &4%%, 

  3                  

 

        

 

 "@%

 ),%('3- '"'330 P'$%('" #%"%%#,#''   F-%-%'#'3-'"%'#!

    

         

  -'%( 9!   "@% -'%( 

  %%#''$ %%( -6 @  +< %( '$ @

''$ ---  ---     ---      ---      

  

  

    

 ),%(' %#',"0 ), ,#<

  

     

 '3-'"'330 '"

Â&#x2014; 254 Â&#x2014;

 ),%( %     ),  ,#''$        --- 

&4%%,        

   





      %   ),%( %%$#  %'2 "!'$%,< ,2I %%%#,#''  % %<    

Â&#x2014; 255 Â&#x2014;


 ),%( @ 0%%(#%$ 5# @ 0 %%(  '$  F" -,  ,#''$                       

 

  

    

  

 



 %%(#%$ 5# @  ),%( %%#''$ %%( -6  @   %%(  '$ @ P'$ #$ -  ':  -# %%# ,#''       P'$#$-,(-# '$- ':-,  ,",#''                   

     

                            

 

       

&4%%,  ---  ---       ---  ---     

(4    ---    ---

       ---    --- 

 --- 



 ---  ---    

 

 

  %  ),%(  "@% 0 -'%( 9!  "@% 0 -'%(  ), ,#''$       &4%%, 

  3                  

 

        

 

 "@%

 ),%('3- '"'330 P'$%('" #%"%%#,#''   F-%-%'#'3-'"%'#!

    

         

  -'%( 9!   "@% -'%( 

  %%#''$ %%( -6 @  +< %( '$ @

''$ ---  ---     ---      ---      

  

  

    

 ),%(' %#',"0 ), ,#<

  

     

 '3-'"'330 '"

Â&#x2014; 254 Â&#x2014;

 ),%( %     ),  ,#''$        --- 

&4%%,        

   





      %   ),%( %%$#  %'2 "!'$%,< ,2I %%%#,#''  % %<    

Â&#x2014; 255 Â&#x2014;


?# %!-4%$  -%(,' (4# !%6'"     

 

              

  

   

     

  

  

  

  -#' (' %  ),%( "!'!. " 0$#. ), ,#''$    

  &4%%,    

                    

      !.!' "$#.0 "  ),%( -#$ " 9' !"#(  5  33 0  #% ' !"#$     5  - ,%#:#'       )#$ " !"# %#6 -'   5  33 0 -1,                      

  

    -#$"9'!"#(#$0  5

                         

  

 ---  --- 0"I%-9'#333Z3 #$6

  

  

 ---   0"I%-9'#33333Z #$6                   > -:

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå VI Ê ïàðàãðàôó 15        0'$#$%$       0'$#$%$   0$#$%$         0$#$%$  @, @, @, @,  &%% #.9'      -            V %%$'2' ' ' '%$-1< ,'-62.6- '9.( 4'''",#''$

            ' '' ' '' 

              

        

   ' '  ' '      

                                  

— 256 —

— 257 —


?# %!-4%$  -%(,' (4# !%6'"     

 

              

  

   

     

  

  

  

  -#' (' %  ),%( "!'!. " 0$#. ), ,#''$    

  &4%%,    

                    

      !.!' "$#.0 "  ),%( -#$ " 9' !"#(  5  33 0  #% ' !"#$     5  - ,%#:#'       )#$ " !"# %#6 -'   5  33 0 -1,                      

  

    -#$"9'!"#(#$0  5

                         

  

 ---  --- 0"I%-9'#333Z3 #$6

  

  

 ---   0"I%-9'#33333Z #$6                   > -:

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå VI Ê ïàðàãðàôó 15        0'$#$%$       0'$#$%$   0$#$%$         0$#$%$  @, @, @, @,  &%% #.9'      -            V %%$'2' ' ' '%$-1< ,'-62.6- '9.( 4'''",#''$

            ' '' ' '' 

              

        

   ' '  ' '      

                                  

— 256 —

— 257 —


 )%. %.".--%(#-.    (4--,#-.% ,9 - %''.   0'-%    0'-%    0-%   0'-%   0-%   0-%   0'-%     0-% T' ('-,                          ),%( #,6,#.6 '  4,  -$,#.6 F"    )     )   2.64'5' )     )  2.64'5' T' ('     ),%(#,!' ' %#' F"        %:%, -1, 

 

           

   =-:.6-9('.6!' '$6        %:   --- ?'-6 

2.6  #'%#'#!9'   2 % --- 0'  

       



2



0

         

0

2

x

â&#x20AC;&#x201C;2

     #' F 5-'9"I,      F 4'-'9"I,     #' F "-'9"I,

       

  ---

          

 

0

1

x

â&#x20AC;&#x201C;1

 

y

0 â&#x20AC;&#x201C;1

        

Â&#x2014; 258 Â&#x2014;

x

y

y

 

  =-#%6 -1,"I'-%%( )   "I-%%( # <   

2



  %  

y

 --- 

Â&#x2014; 259 Â&#x2014;

1

x


 )%. %.".--%(#-.    (4--,#-.% ,9 - %''.   0'-%    0'-%    0-%   0'-%   0-%   0-%   0'-%     0-% T' ('-,                          ),%( #,6,#.6 '  4,  -$,#.6 F"    )     )   2.64'5' )     )  2.64'5' T' ('     ),%(#,!' ' %#' F"        %:%, -1, 

 

           

   =-:.6-9('.6!' '$6        %:   --- ?'-6 

2.6  #'%#'#!9'   2 % --- 0'  

       



2



0

         

0

2

x

â&#x20AC;&#x201C;2

     #' F 5-'9"I,      F 4'-'9"I,     #' F "-'9"I,

       

  ---

          

 

0

1

x

â&#x20AC;&#x201C;1

 

y

0 â&#x20AC;&#x201C;1

        

Â&#x2014; 258 Â&#x2014;

x

y

y

 

  =-#%6 -1,"I'-%%( )   "I-%%( # <   

2



  %  

y

 --- 

Â&#x2014; 259 Â&#x2014;

1

x


                   



8 4 â&#x20AC;&#x201C;8 â&#x20AC;&#x201C;4 0 â&#x20AC;&#x201C;4





        WI -%%$ % %(:    #      % %(: 

y

4

8 x

â&#x20AC;&#x201C;8

    

   

   )  ':$  ) %2%%:$ WI%%!#,6 -$.6

x

   

   WI%%!#,6 -$.6

y

0

 %  

% > WI %% ! #,6 -,-$< .6

â&#x20AC;&#x201C;4 0 â&#x20AC;&#x201C;4

4

   

  WI%%!#,6 -$.6

y

 

x

2 0 â&#x20AC;&#x201C;2

â&#x20AC;&#x201C;5

Â&#x2014; 260 Â&#x2014;

x

1

x

1

x

y

1 0

x

      

 0#'-$#$%$4'   

0

1

4

2

â&#x20AC;&#x201C;4

y

 M M

y

y

0 â&#x20AC;&#x201C;2

   

    WI%%!#,6 -$.6

% =  % > )1, "I # #5 -,< -%% 0 -$$     # -#5 0 -$$    " #-,-$.

 M M

       

 0-'$#$%$4'   

       

  *( . ..)*-  

Â&#x2014; 261 Â&#x2014;


                   



8 4 â&#x20AC;&#x201C;8 â&#x20AC;&#x201C;4 0 â&#x20AC;&#x201C;4





        WI -%%$ % %(:    #      % %(: 

y

4

8 x

â&#x20AC;&#x201C;8

    

   

   )  ':$  ) %2%%:$ WI%%!#,6 -$.6

x

   

   WI%%!#,6 -$.6

y

0

 %  

% > WI %% ! #,6 -,-$< .6

â&#x20AC;&#x201C;4 0 â&#x20AC;&#x201C;4

4

   

  WI%%!#,6 -$.6

y

 

x

2 0 â&#x20AC;&#x201C;2

â&#x20AC;&#x201C;5

Â&#x2014; 260 Â&#x2014;

x

1

x

1

x

y

1 0

x

      

 0#'-$#$%$4'   

0

1

4

2

â&#x20AC;&#x201C;4

y

 M M

y

y

0 â&#x20AC;&#x201C;2

   

    WI%%!#,6 -$.6

% =  % > )1, "I # #5 -,< -%% 0 -$$     # -#5 0 -$$    " #-,-$.

 M M

       

 0-'$#$%$4'   

       

  *( . ..)*-  

Â&#x2014; 261 Â&#x2014;


 ?5 ,-% '$-#.6#,6-$.6

  

        )#-6 ! , ($-$$    0#' )$.-%:%$#'5  

------   ---        L'4'      ---  ---



 ---           ---    ------    

 

     

 ---

 

 

 

  

 

 

–x

2

2 2

x

–2

 

 

y=1–x

— 262 —

  -  ------   -----

2

  -  ------  -----



   ---     ---  --- L'4'

 

 )#,#''%%.#  # 0   )6:  '-      ---  &4'5 %' ' '" % -$. 

%#-:   --- , 

y

2

x

   '4'5-:   

Ê ïàðàãðàôó 16                        

  

        

 

y=x+3

&4'%%. 

   

     0'4'        0%' ''"4'5        0'4'5   



–2 0 –2







y=x–4

 

 

=

y

–2 0

 

&4'%%.     

 

y

–3x y=

 

   &4'5'  

&4'5%' ''"

 ?5 ,-% '$''.6-$.6         )$$  -6 ! , %   

---  ------  

       

 

y = –2x

— 263 —


 ?5 ,-% '$-#.6#,6-$.6

  

        )#-6 ! , ($-$$    0#' )$.-%:%$#'5  

------   ---        L'4'      ---  ---



 ---           ---    ------    

 

     

 ---

 

 

 

  

 

 

–x

2

2 2

x

–2

 

 

y=1–x

— 262 —

  -  ------   -----

2

  -  ------  -----



   ---     ---  --- L'4'

 

 )#,#''%%.#  # 0   )6:  '-      ---  &4'5 %' ' '" % -$. 

%#-:   --- , 

y

2

x

   '4'5-:   

Ê ïàðàãðàôó 16                        

  

        

 

y=x+3

&4'%%. 

   

     0'4'        0%' ''"4'5        0'4'5   



–2 0 –2







y=x–4

 

 

=

y

–2 0

 

&4'%%.     

 

y

–3x y=

 

   &4'5'  

&4'5%' ''"

 ?5 ,-% '$''.6-$.6         )$$  -6 ! , %   

---  ------  

       

 

y = –2x

— 263 —


        

                  



  !   !       !  !       !    !  ! !                               

 

      

       

               



         @ ,  @ ,    @   @ ,

@ @  @ @ @ @   @ , @ , , @ @, ,  

 

                           

      

   

           

                                                                

  

 

           

                         

      

                                  



         

          

                      

   



              







      

 

Â&#x2014; 264 Â&#x2014;

---  ------   

 

   -

 ----





------    

            

---------      ------    

 -

 ----

------    

------   

 

   -----  ------  

  

     

                       

Â&#x2014; 265 Â&#x2014;


        

                  



  !   !       !  !       !    !  ! !                               

 

      

       

               



         @ ,  @ ,    @   @ ,

@ @  @ @ @ @   @ , @ , , @ @, ,  

 

                           

      

   

           

                                                                

  

 

           

                         

      

                                  



         

          

                      

   



              







      

 

Â&#x2014; 264 Â&#x2014;

---  ------   

 

   -

 ----





------    

            

---------      ------    

 -

 ----

------    

------   

 

   -----  ------  

  

     

                       

Â&#x2014; 265 Â&#x2014;




  

â&#x20AC;&#x201C; +  ----------------  ---------------- 



      

        

  

  

  



      

 

('  â&#x20AC;&#x201C; '  â&#x20AC;&#x201C; ( ----------------  ----------------   

('  ( '

( '  '    ( ' (' '  ( ---



                                        

 

          @@  @@,  ,,  ,, @ @,  ,  ,

,@  , , @, ,@  @

     

      

 

  ---  ---   

   

      

 

           &4'5'   

Â&#x2014; 266 Â&#x2014;

  ---  ---  ---      



    &4'5'

  



           



 

 

  

 L!#",#''$ 

(b  ( '

'  '   (  ( ---



   

         

   &4'5' 

   &4'5'  

                

  

     0#'  T' ('

     



 ?5 ,-% '$#5(5-$.6        

        



    

     )#-6-#$-$$ ! ,     0#'#%-$.-< %:%$#'5           

  +,7%#,1          

  +,7%#,1        ------              

 

 ------  ------  +,7%#,1       

Â&#x2014; 267 Â&#x2014;




  

â&#x20AC;&#x201C; +  ----------------  ---------------- 



      

        

  

  

  



      

 

('  â&#x20AC;&#x201C; '  â&#x20AC;&#x201C; ( ----------------  ----------------   

('  ( '

( '  '    ( ' (' '  ( ---



                                        

 

          @@  @@,  ,,  ,, @ @,  ,  ,

,@  , , @, ,@  @

     

      

 

  ---  ---   

   

      

 

           &4'5'   

Â&#x2014; 266 Â&#x2014;

  ---  ---  ---      



    &4'5'

  



           



 

 

  

 L!#",#''$ 

(b  ( '

'  '   (  ( ---



   

         

   &4'5' 

   &4'5'  

                

  

     0#'  T' ('

     



 ?5 ,-% '$#5(5-$.6        

        



    

     )#-6-#$-$$ ! ,     0#'#%-$.-< %:%$#'5           

  +,7%#,1          

  +,7%#,1        ------              

 

 ------  ------  +,7%#,1       

Â&#x2014; 267 Â&#x2014;


    

%  

"  

    ---      ---  ---       --- 

3 5  4   

 ---          ---  ---     ---   

                      ),%(#(%%%(: @ 4  %%< %(:  @ 0      " -,( #'       19-,(#'                % %%(:  @  #( 4    % %%(:@ 0   T!'  !  #$! ''#%-% '-,(-,'%-,'""   0#< $  ! #%-% ' -,(  "  # &%%$'9,-,'%##'   -1,                         ! #%-% ' -,(  %  "  0'-,("#  ),%(  0-7-#"#"-$ F"# -#.5'(!%$  ---  ---  "##50 ---  ---  







 ---  '"'(4 ---  ---  --- ; .#$,%<     #-,  

  ---  ---      ---  ---   

Â&#x2014; 268 Â&#x2014;



                                  

   ""  ),%(.%#' ,'5 2' H-#.5'(#.#!  ---  ---   %%#  

  ---  ---  

H#5'(#.#!    ---   --- 2'



    ---   --- ,'5 %%# 

       ---   ---     ---   ---       



  --- A ---       ---  ---  

 

   ---   ---   

  ---  --- 



  ---  ---      ---  --- 



 

 

  --- 

  

 --- 

  ---  ---   

 

 

  2' ,'5  ),%(-#.5#!"#$ 5# %#< 50 5# % F"    

    

  ---    

  

              

 

            5 ! % !"#$ -#.5 #   50#5

Â&#x2014; 269 Â&#x2014;


    

%  

"  

    ---      ---  ---       --- 

3 5  4   

 ---          ---  ---     ---   

                      ),%(#(%%%(: @ 4  %%< %(:  @ 0      " -,( #'       19-,(#'                % %%(:  @  #( 4    % %%(:@ 0   T!'  !  #$! ''#%-% '-,(-,'%-,'""   0#< $  ! #%-% ' -,(  "  # &%%$'9,-,'%##'   -1,                         ! #%-% ' -,(  %  "  0'-,("#  ),%(  0-7-#"#"-$ F"# -#.5'(!%$  ---  ---  "##50 ---  ---  







 ---  '"'(4 ---  ---  --- ; .#$,%<     #-,  

  ---  ---      ---  ---   

Â&#x2014; 268 Â&#x2014;



                                  

   ""  ),%(.%#' ,'5 2' H-#.5'(#.#!  ---  ---   %%#  

  ---  ---  

H#5'(#.#!    ---   --- 2'



    ---   --- ,'5 %%# 

       ---   ---     ---   ---       



  --- A ---       ---  ---  

 

   ---   ---   

  ---  --- 



  ---  ---      ---  --- 



 

 

  --- 

  

 --- 

  ---  ---   

 

 

  2' ,'5  ),%(-#.5#!"#$ 5# %#< 50 5# % F"    

    

  ---    

  

              

 

            5 ! % !"#$ -#.5 #   50#5

Â&#x2014; 269 Â&#x2014;


 T!' '-%''. % !  )%,# < '$ ' / -# % %' #'         # %-%,'(4'$'/   )1,

      

   

      

   

 

    

 

   

   ---    

   # 4 % % .  "  # 4 % -4< ' 0"

    ) 7,: -7( 6 ,"# !  " ---  0 

-7( " ,"  ---  0 -7( (4" ,"  ),%( 0-7(,:%%(!''( $ #%  0 % %2# #   F" -7((4","#' ---  --- -7(<



"0 ---  --- '%2!'(%%-<  7( #',: ---  F ! -,  %%,

,#''5   ---  ---  ---     

 ---  ---  ---   

 ),%( "%%'"4%% "0%% '"4%-4' +%#%%,,#''5       

                                

 

 

 ),%( ' -# %' !"#$  5 # '(  '# 0 F"''6#%"!"#

  5 -,%#:#'  5 +%#-< #,#''

   )%,%#4'%##'$'-#%'!"#$   5'#0  5 H%"!"#      -,%< #:#' +%##,#''      

    

             

 

   

   

         5 # '( !"#$ ' 3 %'   50'33

 ---  --- 

 ---  ---        

+ 

--------------------  ---       

 --- 

 --- 

  ---   



--------------    ----------------       â&#x20AC;&#x201C; 

 â&#x20AC;&#x201C; -----

 --- 

 --- 

 --- 

 

--------------        #. %2#

Â&#x2014; 270 Â&#x2014;

Â&#x2014; 271 Â&#x2014;


 T!' '-%''. % !  )%,# < '$ ' / -# % %' #'         # %-%,'(4'$'/   )1,

      

   

      

   

 

    

 

   

   ---    

   # 4 % % .  "  # 4 % -4< ' 0"

    ) 7,: -7( 6 ,"# !  " ---  0 

-7( " ,"  ---  0 -7( (4" ,"  ),%( 0-7(,:%%(!''( $ #%  0 % %2# #   F" -7((4","#' ---  --- -7(<



"0 ---  --- '%2!'(%%-<  7( #',: ---  F ! -,  %%,

,#''5   ---  ---  ---     

 ---  ---  ---   

 ),%( "%%'"4%% "0%% '"4%-4' +%#%%,,#''5       

                                

 

 

 ),%( ' -# %' !"#$  5 # '(  '# 0 F"''6#%"!"#

  5 -,%#:#'  5 +%#-< #,#''

   )%,%#4'%##'$'-#%'!"#$   5'#0  5 H%"!"#      -,%< #:#' +%##,#''      

    

             

 

   

   

         5 # '( !"#$ ' 3 %'   50'33

 ---  --- 

 ---  ---        

+ 

--------------------  ---       

 --- 

 --- 

  ---   



--------------    ----------------       â&#x20AC;&#x201C; 

 â&#x20AC;&#x201C; -----

 --- 

 --- 

 --- 

 

--------------        #. %2#

Â&#x2014; 270 Â&#x2014;

Â&#x2014; 271 Â&#x2014;


ÇÀÄÀ×È ÏÎÂÛØÅÍÍÎÉ ÒÐÓÄÍÎÑÒÈ

  ------   

 +%#%%,,#''5        ------     -------  -------      

 

  ?5 !,#''$    ---------- F –



            

-,%#: 0',('. %9' .(',('. %                M M     M  M          M M           M M      N'' %  #                   ),%( 0 %##.#95  H-#5  %' %  

#.!

 

 

#. H#5 %' %  

#.!    

   %##.# 6%%('#.  ),%(  0 ' -$,"('   0 " 4' F"          -7( -$,"(' ,# %$' /  T!'  !   %6##-#( $76 F"             

          

             #-#$70 6###0  6#(06#

— 272 —

  

         

  ---------    ------  F-(9''5 ------



    



                                          F"      

 *%-,%#:!-%.#%$#%,:7#  )-9 #% %:' < '. F" %' '-!#'#,6' < '.6 % %, '%,#,6' < '.6 %  ? %  - --9': ' '  -# #'%#,    #% %:'",.(' '.  ),%(  0 2I %$#   0 2I '2 %< " %  +%# ,#''            _I9-'< ( !' '$     - 1 -, :%$ %        

— 273 —


ÇÀÄÀ×È ÏÎÂÛØÅÍÍÎÉ ÒÐÓÄÍÎÑÒÈ

  ------   

 +%#%%,,#''5        ------     -------  -------      

 

  ?5 !,#''$    ---------- F –



            

-,%#: 0',('. %9' .(',('. %                M M     M  M          M M           M M      N'' %  #                   ),%( 0 %##.#95  H-#5  %' %  

#.!

 

 

#. H#5 %' %  

#.!    

   %##.# 6%%('#.  ),%(  0 ' -$,"('   0 " 4' F"          -7( -$,"(' ,# %$' /  T!'  !   %6##-#( $76 F"             

          

             #-#$70 6###0  6#(06#

— 272 —

  

         

  ---------    ------  F-(9''5 ------



    



                                          F"      

 *%-,%#:!-%.#%$#%,:7#  )-9 #% %:' < '. F" %' '-!#'#,6' < '.6 % %, '%,#,6' < '.6 %  ? %  - --9': ' '  -# #'%#,    #% %:'",.(' '.  ),%(  0 2I %$#   0 2I '2 %< " %  +%# ,#''            _I9-'< ( !' '$     - 1 -, :%$ %        

— 273 —


    ccc )#.5%'9<

!

!

(1"-!#'$%$' %%!

,76-$'2 H5%'9(%9

'2:.%%'!.6!'.#%(: ',$  -1, 9 %$ '  '-'  %%$' #(#%, %%,< "2I%$'  F!'' % %$'     &!-% %''%%'(2 "2> T #' '%2 -2-,  '(   -% %'< %$' "'9.( U:',('%%#' %'(4%$ -5'5''! %  F   --9# 20%%#' %! #'%#'(2!:  '%$-5< '5''! %  #--% %' L --9'    % 2 $#$%$ %< %#'. %-#-# :-1, %< 2-%#''-'  %' $#$%$'-%.'%%#'.  K, !' ( % #,!' ' % !

 )#' (' %

-%-%'#-, 

)1, 

                    

      

  

     

  

   WI ,#''$ $#$%$\'' -$.6   

y

2 â&#x20AC;&#x201C;4 â&#x20AC;&#x201C;2 0 â&#x20AC;&#x201C;2

      % %#'  8% 0%#,!' ' %     H-#%,        "'9.(-%(,  '-'  0%$ '$2I H#%,         )    L!< ',-#,:2I,#:! %  

Â&#x2014; 274 Â&#x2014;

2

4

6

4

6

x y = â&#x20AC;&#x201C;3

â&#x20AC;&#x201C;4   

  

  

  WI,#''$ $#$%$ \'' -$.6      %  

y 4

x=0

2 â&#x20AC;&#x201C;4 â&#x20AC;&#x201C;2 0 â&#x20AC;&#x201C;2

  %#%$ $ " . ' %-,( %  % -!#'   Q'" ' !' :%$  '"< !' '. % F",%#! !-4%$##                   

x=2

4

2

8

x

â&#x20AC;&#x201C;4 y = â&#x20AC;&#x201C;x

  M M  FM M -  - -,     --- ) >

M M           

 F!"I,#< ''$ %% ! 2< ('5 -,%    -< ,-$5   =

Â&#x2014; 275 Â&#x2014;

y 4 2 â&#x20AC;&#x201C;2 0 â&#x20AC;&#x201C;2 â&#x20AC;&#x201C;4

2

4

6

x


    ccc )#.5%'9<

!

!

(1"-!#'$%$' %%!

,76-$'2 H5%'9(%9

'2:.%%'!.6!'.#%(: ',$  -1, 9 %$ '  '-'  %%$' #(#%, %%,< "2I%$'  F!'' % %$'     &!-% %''%%'(2 "2> T #' '%2 -2-,  '(   -% %'< %$' "'9.( U:',('%%#' %'(4%$ -5'5''! %  F   --9# 20%%#' %! #'%#'(2!:  '%$-5< '5''! %  #--% %' L --9'    % 2 $#$%$ %< %#'. %-#-# :-1, %< 2-%#''-'  %' $#$%$'-%.'%%#'.  K, !' ( % #,!' ' % !

 )#' (' %

-%-%'#-, 

)1, 

                    

      

  

     

  

   WI ,#''$ $#$%$\'' -$.6   

y

2 â&#x20AC;&#x201C;4 â&#x20AC;&#x201C;2 0 â&#x20AC;&#x201C;2

      % %#'  8% 0%#,!' ' %     H-#%,        "'9.(-%(,  '-'  0%$ '$2I H#%,         )    L!< ',-#,:2I,#:! %  

Â&#x2014; 274 Â&#x2014;

2

4

6

4

6

x y = â&#x20AC;&#x201C;3

â&#x20AC;&#x201C;4   

  

  

  WI,#''$ $#$%$ \'' -$.6      %  

y 4

x=0

2 â&#x20AC;&#x201C;4 â&#x20AC;&#x201C;2 0 â&#x20AC;&#x201C;2

  %#%$ $ " . ' %-,( %  % -!#'   Q'" ' !' :%$  '"< !' '. % F",%#! !-4%$##                   

x=2

4

2

8

x

â&#x20AC;&#x201C;4 y = â&#x20AC;&#x201C;x

  M M  FM M -  - -,     --- ) >

M M           

 F!"I,#< ''$ %% ! 2< ('5 -,%    -< ,-$5   =

Â&#x2014; 275 Â&#x2014;

y 4 2 â&#x20AC;&#x201C;2 0 â&#x20AC;&#x201C;2 â&#x20AC;&#x201C;4

2

4

6

x


  M M  y )    -,  M M -1,    ,<    ) â&#x20AC;&#x201C;1  >   M M    0 -1,     ,  y = â&#x20AC;&#x201C;1     -%(, - ,%#: >

F! ---       ---    

x=1 y=0 x

1

L%.5"I%%!%  -,< -$.6  >  =  

y

 F  % ' #%$' Q'< " ' ' #%$' -1, ' #%$ ' N     -%'$$2I % %#-%%#(' % '< #%$' F!-%'$$2I %  #'%,-%'62I %  -1, %

  ' #%$',   %$'

y = |x| â&#x20AC;&#x201C; 3 

0

â&#x20AC;&#x201C;3

3

y

x

(

)

(

)

C 1 â&#x20AC;&#x201C;x; â&#x20AC;&#x201C;2y 2

y = 4 â&#x20AC;&#x201C; |x| 4

x

)

D â&#x20AC;&#x201C;1 â&#x20AC;&#x201C;x; â&#x20AC;&#x201C;1 â&#x20AC;&#x201C;y 2 23

4

0

M(x; y)

0

(

y

â&#x20AC;&#x201C;4

A(2x; 2y)

1 B â&#x20AC;&#x201C;3x; â&#x20AC;&#x201C;y 2

â&#x20AC;&#x201C;3 



   %  %$ '   '   )%(, %  $#$%$ ,  ' $!' (%$ '    '" ' %  $#$:7%$ # $!< ' (%$'  L'(' %#< '  





 +  + --------------------- " --------------------- T!' %   

x





+

   

+

 

+  ++

-  ------------------------------  ---------------------  F"% -------------------------------   

 ),%(  0 % ',(' % "   

+



+



+

Q'" '" -------------------    + 

 "0',('. % ---  

-  = ---------------------   % = " % = "   )%(, ------------------- 

 ---  F %0',('%:%,< 

-#$((4#5

  %$' 0' ?" %$ '0' 

Â&#x2014; 276 Â&#x2014;



+



+

              

Â&#x2014; 277 Â&#x2014;


  M M  y )    -,  M M -1,    ,<    ) â&#x20AC;&#x201C;1  >   M M    0 -1,     ,  y = â&#x20AC;&#x201C;1     -%(, - ,%#: >

F! ---       ---    

x=1 y=0 x

1

L%.5"I%%!%  -,< -$.6  >  =  

y

 F  % ' #%$' Q'< " ' ' #%$' -1, ' #%$ ' N     -%'$$2I % %#-%%#(' % '< #%$' F!-%'$$2I %  #'%,-%'62I %  -1, %

  ' #%$',   %$'

y = |x| â&#x20AC;&#x201C; 3 

0

â&#x20AC;&#x201C;3

3

y

x

(

)

(

)

C 1 â&#x20AC;&#x201C;x; â&#x20AC;&#x201C;2y 2

y = 4 â&#x20AC;&#x201C; |x| 4

x

)

D â&#x20AC;&#x201C;1 â&#x20AC;&#x201C;x; â&#x20AC;&#x201C;1 â&#x20AC;&#x201C;y 2 23

4

0

M(x; y)

0

(

y

â&#x20AC;&#x201C;4

A(2x; 2y)

1 B â&#x20AC;&#x201C;3x; â&#x20AC;&#x201C;y 2

â&#x20AC;&#x201C;3 



   %  %$ '   '   )%(, %  $#$%$ ,  ' $!' (%$ '    '" ' %  $#$:7%$ # $!< ' (%$'  L'(' %#< '  





 +  + --------------------- " --------------------- T!' %   

x





+

   

+

 

+  ++

-  ------------------------------  ---------------------  F"% -------------------------------   

 ),%(  0 % ',(' % "   

+



+



+

Q'" '" -------------------    + 

 "0',('. % ---  

-  = ---------------------   % = " % = "   )%(, ------------------- 

 ---  F %0',('%:%,< 

-#$((4#5

  %$' 0' ?" %$ '0' 

Â&#x2014; 276 Â&#x2014;



+



+

              

Â&#x2014; 277 Â&#x2014;


        ---        --- 

 -     ---     ---            ---       ----

    ---   ---  

H.9' # %6 '2('   ' $#< $%$%,5#,6###'',:(-   ---     ---       -       ? - ,%<

#: 6$.'! % '',$-1,        ---    ---   =

           

        =   $#%6  

  

                                                                                                         '     '  '    )%(, ' 0 -% % (4'' '-1, %''$#< $:%$-%#('. '. %'!#,6 -%#('.6 '.6 % ' $!(' < %$ '-1,-!#'''%$'  +,"5%'.'' '< -' '=-1,'%$'#%,-< %. %' H-#%, ''   ##0''          # 6 %, $6 -!#'

Â&#x2014; 278 Â&#x2014;

' '%$' F1-!#'< %$7'  % ':76< 5'%$'                            8%-!#'   $#$%$#<  2" %  %     $!' (%$ '    ' #(%$' ''" 9' ' #(%$''  "'9.( #. 2.6 % ' #:%$ ( 2I     U:',(' %''9'!-%( ## "0',(' % F"<                           # 6 %, $6 ,!''$ !< '%('                        c            N'',#''9'!-%(#%,:7#       8% %   '.' '.%'< 9     '.-!#'     %$'' %'%$'-1,#'< %#'#!9' 8%9'! %   ' ,"' '%'9    ' '. -!#'        ' ' ' %  '  -#  #'%#,   F ! ,#'< ''4'5#2.6 %6  )-9 2. %%,7%#,< : F"%-##.#'%#        

Â&#x2014; 279 Â&#x2014;


        ---        --- 

 -     ---     ---            ---       ----

    ---   ---  

H.9' # %6 '2('   ' $#< $%$%,5#,6###'',:(-   ---     ---       -       ? - ,%<

#: 6$.'! % '',$-1,        ---    ---   =

           

        =   $#%6  

  

                                                                                                         '     '  '    )%(, ' 0 -% % (4'' '-1, %''$#< $:%$-%#('. '. %'!#,6 -%#('.6 '.6 % ' $!(' < %$ '-1,-!#'''%$'  +,"5%'.'' '< -' '=-1,'%$'#%,-< %. %' H-#%, ''   ##0''          # 6 %, $6 -!#'

Â&#x2014; 278 Â&#x2014;

' '%$' F1-!#'< %$7'  % ':76< 5'%$'                            8%-!#'   $#$%$#<  2" %  %     $!' (%$ '    ' #(%$' ''" 9' ' #(%$''  "'9.( #. 2.6 % ' #:%$ ( 2I     U:',(' %''9'!-%( ## "0',(' % F"<                           # 6 %, $6 ,!''$ !< '%('                        c            N'',#''9'!-%(#%,:7#       8% %   '.' '.%'< 9     '.-!#'     %$'' %'%$'-1,#'< %#'#!9' 8%9'! %   ' ,"' '%'9    ' '. -!#'        ' ' ' %  '  -#  #'%#,   F ! ,#'< ''4'5#2.6 %6  )-9 2. %%,7%#,< : F"%-##.#'%#        

Â&#x2014; 279 Â&#x2014;


H. $-#,#''%%.!#"-,          

                 F#.9'#%6-2.6$#$%$ 2. %-%'#'%#!'  < %$' '#!9' L--9'%,< 7%##'2.6,##$:76,%#: !  -#  -# : -1, 6 2.6 1II2'#'%,7%#,     !  !  !      !      !   !   !       !      !    !    !  !   !  !  !  !  +! - !<   !  !  -  ---------- '%( !  #'',:  P-4'',#''## '('((   8%( '  (    ,' 8%9(= '=(= !'(0' < '.-%. % F"'9'('(#< #5 %,#''$ '.-!#''('( %$' ? ' %(9'-%#(##    "  0 ' ',(' % - 1 (      &< #'%#(  !'   %(  -''#%    '%$' L-(= #'%#'#!9'%#(' ,#'''%#''4''(

&4 -, '',: %%, '5'.6 ,#''5 #"< $%(%#6,#'! )#,#'',94' L!#< "'6   L!(" ,#''$9''5;          L''2!-%'" ,#''$'6               N$" .4(! ,',9''51II2'. -.6#'%#       

$#$%$9%# )!, #,: %( 1" #'%#                        L#'%#        

9'.(9%# -1,1II2'.-'#.6%-'$6 #'.         ;        T' ('-,   

        â&#x20AC;&#x201C; 

- T%:%,  

 H.!  !   -----------------

9' (%$ '   #!9' ( -   

 N# '" ' 9%#'' #'. % #'. 1I< I2'.-'#.6%-'$6-''5  )1, -!, -#,: %( ''" #'%#  -#'$1II2'.-%#%#,:76%-'$6                                        

    !  !  +9##%,#''$%%.-,    F"!-#",#''$'5   !-%'"!       !

Â&#x2014; 280 Â&#x2014;

Â&#x2014; 281 Â&#x2014;

 â&#x20AC;&#x201C; -----------------------  ------  "   



   


H. $-#,#''%%.!#"-,          

                 F#.9'#%6-2.6$#$%$ 2. %-%'#'%#!'  < %$' '#!9' L--9'%,< 7%##'2.6,##$:76,%#: !  -#  -# : -1, 6 2.6 1II2'#'%,7%#,     !  !  !      !      !   !   !       !      !    !    !  !   !  !  !  !  +! - !<   !  !  -  ---------- '%( !  #'',:  P-4'',#''## '('((   8%( '  (    ,' 8%9(= '=(= !'(0' < '.-%. % F"'9'('(#< #5 %,#''$ '.-!#''('( %$' ? ' %(9'-%#(##    "  0 ' ',(' % - 1 (      &< #'%#(  !'   %(  -''#%    '%$' L-(= #'%#'#!9'%#(' ,#'''%#''4''(

&4 -, '',: %%, '5'.6 ,#''5 #"< $%(%#6,#'! )#,#'',94' L!#< "'6   L!(" ,#''$9''5;          L''2!-%'" ,#''$'6               N$" .4(! ,',9''51II2'. -.6#'%#       

$#$%$9%# )!, #,: %( 1" #'%#                        L#'%#        

9'.(9%# -1,1II2'.-'#.6%-'$6 #'.         ;        T' ('-,   

        â&#x20AC;&#x201C; 

- T%:%,  

 H.!  !   -----------------

9' (%$ '   #!9' ( -   

 N# '" ' 9%#'' #'. % #'. 1I< I2'.-'#.6%-'$6-''5  )1, -!, -#,: %( ''" #'%#  -#'$1II2'.-%#%#,:76%-'$6                                        

    !  !  +9##%,#''$%%.-,    F"!-#",#''$'5   !-%'"!       !

Â&#x2014; 280 Â&#x2014;

Â&#x2014; 281 Â&#x2014;

 â&#x20AC;&#x201C; -----------------------  ------  "   



   


   ! !  )% %9'$ #%6 ,#''5 %%. -,      !,  ! F-(9'"'5<   !   !   !   !        !  ?,(' %$#$%$'#''#<   , #' 4%5 %-' '" ',< ('" % F!   )    %    $#$%$ '!' '.  -   % $#$%$#,!' '. P'  0'< %#'' % ,##$:7 ,%#: !  - 1   L%. %#'.    "',('. %

 ':765 F"     

  &4'$-%'",#''$$#$:%$-.

       -.        ,9%. % (#,"-$ L%. %#'.                   

      ),%( @ 0%%(2%#", @ 0 %%(2%-", F"-,%#:!< 9'%%#(%,:7,:%%,,#''5     ---  ---  ------  ------ 



     ---  ---  ------  ------  





- )%#!' ' #-#,#''%%<  -------------  â&#x20AC;&#x201C;

  â&#x20AC;&#x201C;    -  ---  ------  

   . ---  -------------------------- 





    @ 

      -  ------------------  ----------------- @ F"  -------------  â&#x20AC;&#x201C;

 â&#x20AC;&#x201C; 

  @ @  ),%( 0#!% 0#!%%%. +%# %%,,#''5

  B   

    

   

  

  

  

  

                    ),%(  @  0 %%( #,%  @  0 %%( "#"#$ Q#,%#(#%%(    -  --- !  %-%#.!-1, ----------- +

8%.#,%#.4#  '#(#  '#,%6.  %'!# < ' % #,%  #( #"%( . '#% , â&#x20AC;&#x201C; 

---------------------------  ,",",     

+

&4-, '',:%%,,#''5    -------------  --- 

+

                          



  @  @  ),%(  @  0 %%( #%-%  @  0 %<

)%#. '$-#",#''$!#"-, 

------ @ 0%%(#" %(-#"#,%" 

      ---  ---  ------  ---  ---  ------           





#,%  N #%  % -#. #,% #%-% 6  '%#.0 -1,9'%%<

Â&#x2014; 282 Â&#x2014;



Â&#x2014; 283 Â&#x2014;


   ! !  )% %9'$ #%6 ,#''5 %%. -,      !,  ! F-(9'"'5<   !   !   !   !        !  ?,(' %$#$%$'#''#<   , #' 4%5 %-' '" ',< ('" % F!   )    %    $#$%$ '!' '.  -   % $#$%$#,!' '. P'  0'< %#'' % ,##$:7 ,%#: !  - 1   L%. %#'.    "',('. %

 ':765 F"     

  &4'$-%'",#''$$#$:%$-.

       -.        ,9%. % (#,"-$ L%. %#'.                   

      ),%( @ 0%%(2%#", @ 0 %%(2%-", F"-,%#:!< 9'%%#(%,:7,:%%,,#''5     ---  ---  ------  ------ 



     ---  ---  ------  ------  





- )%#!' ' #-#,#''%%<  -------------  â&#x20AC;&#x201C;

  â&#x20AC;&#x201C;    -  ---  ------  

   . ---  -------------------------- 





    @ 

      -  ------------------  ----------------- @ F"  -------------  â&#x20AC;&#x201C;

 â&#x20AC;&#x201C; 

  @ @  ),%( 0#!% 0#!%%%. +%# %%,,#''5

  B   

    

   

  

  

  

  

                    ),%(  @  0 %%( #,%  @  0 %%( "#"#$ Q#,%#(#%%(    -  --- !  %-%#.!-1, ----------- +

8%.#,%#.4#  '#(#  '#,%6.  %'!# < ' % #,%  #( #"%( . '#% , â&#x20AC;&#x201C; 

---------------------------  ,",",     

+

&4-, '',:%%,,#''5    -------------  --- 

+

                          



  @  @  ),%(  @  0 %%( #%-%  @  0 %<

)%#. '$-#",#''$!#"-, 

------ @ 0%%(#" %(-#"#,%" 

      ---  ---  ------  ---  ---  ------           





#,%  N #%  % -#. #,% #%-% 6  '%#.0 -1,9'%%<

Â&#x2014; 282 Â&#x2014;



Â&#x2014; 283 Â&#x2014;


 -------------  

+

#( %%, ,#''5

   ---   

   --------------------  ---   

+ ------ 

"%,6"#7%# "#. +%#,#''

   ------  

  

-------------------         

    

    



 +

 

      

 -------------------------  --------------------  -----------------  ------------ " D%<

  





%.5''.,"$,# %('   "

  

    ---    

  "

  @  T!'  ! @  @ %%#%'-< 46 F"%%$'%"#' ---  ---   ---

  ---

---

  -  -------  --F-(9'%%#(-#,#'' ----- 

-%%7'$' ---  ---   N#%< 

 ),%( @'0%%(6(.(# @'0 %%( " <"   *!   ' -% #.6 ! 4. ($ -4   #  V %%$' <5 ---------- ', P1#$ <5-< -9! 

 ----------   -------------  #  P'  %%$' 9, 4 ---   

($#'"<5' "'$( <"

%-46#%'-6%%$'   ---    

  +  -------------  -------------------------------- # <5"< %%#$  

 -46-4   ---   -1#%'-<  46-,!''.%%$'$!'9 #$ 

'$ <" % %%(:   ---  -1, #$! 

--- + --- â&#x20AC;&#x201C; --- + --- â&#x20AC;&#x201C;     - ---------------  --------------- , .#$    ---------------  --------------

 ---

)%%7'$'  -%.%,! -,   ------  ---   ------   ------  @    

 ---  ---  @ 

 â&#x20AC;&#x201C; ---  

!<5'"4.'%%#<   +  ----------   --------------------------------  H% 1 #$ <5  4 # $ 

 â&#x20AC;&#x201C; 

&%%$'%"#' ---  ---   

  @ @  H( .5'',"$%9%(    "#. 

"%,6"#7%# )% #,6'('" -.#'$ ' #!,6 ,"( %9

Â&#x2014; 284 Â&#x2014;

----------   ! ''  . '  -4 ' ---  

 +  --------------------------------  #'(4 %#. V4<  

  â&#x20AC;&#x201C; 

'5 -,( ($ - % %%(:  @'  



 +  -------------------------------- H%#$< '"' <"#' 

  --- ---     ---      

+

  +    ----------  --------------------------------   ----------  ---  ------------------------  ', ! ---  ---  

  

 â&#x20AC;&#x201C; 

 â&#x20AC;&#x201C; 

-,%#:#'', +



 ----------   ----------------   ----------  ----------------     L 

 

â&#x20AC;&#x201C;

â&#x20AC;&#x201C;

     -#.59.%#! 4

Â&#x2014; 285 Â&#x2014;


 -------------  

+

#( %%, ,#''5

   ---   

   --------------------  ---   

+ ------ 

"%,6"#7%# "#. +%#,#''

   ------  

  

-------------------         

    

    



 +

 

      

 -------------------------  --------------------  -----------------  ------------ " D%<

  





%.5''.,"$,# %('   "

  

    ---    

  "

  @  T!'  ! @  @ %%#%'-< 46 F"%%$'%"#' ---  ---   ---

  ---

---

  -  -------  --F-(9'%%#(-#,#'' ----- 

-%%7'$' ---  ---   N#%< 

 ),%( @'0%%(6(.(# @'0 %%( " <"   *!   ' -% #.6 ! 4. ($ -4   #  V %%$' <5 ---------- ', P1#$ <5-< -9! 

 ----------   -------------  #  P'  %%$' 9, 4 ---   

($#'"<5' "'$( <"

%-46#%'-6%%$'   ---    

  +  -------------  -------------------------------- # <5"< %%#$  

 -46-4   ---   -1#%'-<  46-,!''.%%$'$!'9 #$ 

'$ <" % %%(:   ---  -1, #$! 

--- + --- â&#x20AC;&#x201C; --- + --- â&#x20AC;&#x201C;     - ---------------  --------------- , .#$    ---------------  --------------

 ---

)%%7'$'  -%.%,! -,   ------  ---   ------   ------  @    

 ---  ---  @ 

 â&#x20AC;&#x201C; ---  

!<5'"4.'%%#<   +  ----------   --------------------------------  H% 1 #$ <5  4 # $ 

 â&#x20AC;&#x201C; 

&%%$'%"#' ---  ---   

  @ @  H( .5'',"$%9%(    "#. 

"%,6"#7%# )% #,6'('" -.#'$ ' #!,6 ,"( %9

Â&#x2014; 284 Â&#x2014;

----------   ! ''  . '  -4 ' ---  

 +  --------------------------------  #'(4 %#. V4<  

  â&#x20AC;&#x201C; 

'5 -,( ($ - % %%(:  @'  



 +  -------------------------------- H%#$< '"' <"#' 

  --- ---     ---      

+

  +    ----------  --------------------------------   ----------  ---  ------------------------  ', ! ---  ---  

  

 â&#x20AC;&#x201C; 

 â&#x20AC;&#x201C; 

-,%#:#'', +



 ----------   ----------------   ----------  ----------------     L 

 

â&#x20AC;&#x201C;

â&#x20AC;&#x201C;

     -#.59.%#! 4

Â&#x2014; 285 Â&#x2014;


Îãëàâëåíèå

Ãëàâà V ÔÎÐÌÓËÛ ÑÎÊÐÀÙÅÍÍÎÃÎ ÓÌÍÎÆÅÍÈß             



d G#%,.#!'%             d &!'%(## +,!'%(,#     d )!#'2.6#.9'5              N-'('.,-9''$"#Z              

    

à ë à â à VI Ãëàâà I ÂÛÐÀÆÅÍÈß, ÒÎÆÄÅÑÒÂÀ, ÓÐÀÂÍÅÍÈß               



d H.9'$                                 d )!#'#.9'5                    d ;#''$%'5-''5                  N-'('.,-9''$"#3              

 

 

ÑÈÑÒÅÌÛ ËÈÍÅÉÍÛÕ ÓÐÀÂÍÅÍÈÉ                  

d U'5'.,#''$%#,$-''. 6%%.                                    d &4'%%'5'.6,#''5            N-'('.,-9''$"#Z3             

 

Çàäà÷è ïîâûøåííîé òðóäíîñòè                     



à ë à â à II ÔÓÍÊÖÈÈ                                     



d `,'26"I                         d U'5'$I,'2$                           N-'('.,-9''$"#33             

  

à ë à â à III ÑÒÅÏÅÍÜ Ñ ÍÀÒÓÐÀËÜÍÛÌ ÏÎÊÀÇÀÒÅËÅÌ             



d +-'(%#5%#                         d T' '.                                  d Q%:'$'%('$-"4'%         N-'('.,-9''$"#333             



  

à ë à â à IV ÌÍÎÃÎ×ËÅÍÛ                                 



d +,!'%('" '#                  d )!#'' ''" '           d )!#''" '#                     N-'('.,-9''$"#3Z             



    

— 286 —

— 287 —


Îãëàâëåíèå

Ãëàâà V ÔÎÐÌÓËÛ ÑÎÊÐÀÙÅÍÍÎÃÎ ÓÌÍÎÆÅÍÈß             



d G#%,.#!'%             d &!'%(## +,!'%(,#     d )!#'2.6#.9'5              N-'('.,-9''$"#Z              

    

à ë à â à VI Ãëàâà I ÂÛÐÀÆÅÍÈß, ÒÎÆÄÅÑÒÂÀ, ÓÐÀÂÍÅÍÈß               



d H.9'$                                 d )!#'#.9'5                    d ;#''$%'5-''5                  N-'('.,-9''$"#3              

 

 

ÑÈÑÒÅÌÛ ËÈÍÅÉÍÛÕ ÓÐÀÂÍÅÍÈÉ                  

d U'5'.,#''$%#,$-''. 6%%.                                    d &4'%%'5'.6,#''5            N-'('.,-9''$"#Z3             

 

Çàäà÷è ïîâûøåííîé òðóäíîñòè                     



à ë à â à II ÔÓÍÊÖÈÈ                                     



d `,'26"I                         d U'5'$I,'2$                           N-'('.,-9''$"#33             

  

à ë à â à III ÑÒÅÏÅÍÜ Ñ ÍÀÒÓÐÀËÜÍÛÌ ÏÎÊÀÇÀÒÅËÅÌ             



d +-'(%#5%#                         d T' '.                                  d Q%:'$'%('$-"4'%         N-'('.,-9''$"#333             



  

à ë à â à IV ÌÍÎÃÎ×ËÅÍÛ                                 



d +,!'%('" '#                  d )!#'' ''" '           d )!#''" '#                     N-'('.,-9''$"#3Z             



    

— 286 —

— 287 —


Учебное издание

Решение задач из учебника Ю. Н. Макарычева, Н. Г. Миндюк, К. И. Нешкова, С. Б. Суворовой «Алгебра. 7 класс» Автор-составитель Луканов Николай Дмитриевич Ответственный редактор Н. В. Валуева Младший редактор К. А. Каширина Технический редактор Л. Б. Чуева Оригинал-макет подготовлен ООО «Бета-Фрейм» Подписано в печать 20.07.2005. Формат 84х1081/32 . Гарнитура «Литературная». Печать офсетная. Усл. печ. л. 15,12. Тираж 5000 экз. Заказ № . Общероссийский классификатор продукции ОК-005-93, том 2; 953005 — учебная литература ООО «Издательство Оникс». 127422, Москва, ул. Тимирязевская, д. 38/25. Почтовый адрес: 117418, Москва, а/я 26. Отдел реализации: тел. (095) 310-75-25, 110-02-50. Internet: www.onyx.ru; e-mail: mail@onyx.ru ООО «Издательство «Мир и Образование». Изд. лиц. ИД № 05088 от 18.06.2001. 109193, Москва, ул. 5-я Кожуховская, д. 13, стр. 1. Тел./факс (095) 120-51-47, 129-09-60, 742-43-54. E-mail: mir-obrazovanie@onyx.ru

MakarycevMindyukNeshkovaReshenieZadacAlgebra7klass2004  

(a + b) 2 = a 2 + 2ab + b 2 a 3 + b 3 = (a + b)(a 2 ab + b 2 ) Москва ОНИКС Мир и Образование 2005 a n : a k = a n k a n : a k = a n k a n...

Advertisement