43 + 432 − 1800 43 − 432 − 1800 + + 2 2
43 + 30 2 + 43 − 30 2 =
109.
43 + 432 − 1800 43 − 432 − 1800 43 − 1849 − 1800 43 + 49 − =2 =2 = 2 2 2 2
+ =2
43 + 7 50 =2 = 2 25 = 10 . 2 2
110. a = (4 − 3 2)2 + 8 34 − 24 2 − 5 = 16 − 24 2 + 18 + 34 + 1156 − 1152 34 + 1156 − 1152 + 8 − 2 2
− 5 = 34 −
− 24 2 + 8 ⋅ (3 2 − 4) − 5 = 34 − 24 2 + 24 2 − 32 − 5 = = 2 − 5 ; 2 − 5 < 0 , так как 2 < 5 , значит, a < 0 . 2
111. 1) a = b=
5− 3
2
+
5 3+ 2 2
2
;
5− 3
2) a = 2 + 3 ; значит, a < b ;
2 < 1,4143;
4) a = 13 − 12 ; 13 < 3,604; a < 0,14 < 0,147 < b .
=
2 2− 3
5
=
5 + 10
=
2( 2 + 3 )
5 (5 − 10 ) (5 − 10 )(5 + 10 )
=
17 < 4,124; b < 1,124 < 1,127 < a ,
12 > 3,464;
( 2 − 3 )( 2 + 3 )
5 5 ( 5 )2 ⋅ 2 5 5 − 5 2 = = 15 15
=
4⋅ 2
5) =
3 4
5 −4 2
=
3
8
3
11 < 3,317;
2( 2 + 3 ) = −2( 2 + 3 ) ; 2−3
5 (5 − 10 ) = 25 − 10
5 (5 − 10 ) = 15
5− 2 ; 3
3 3 3 3 3) 3 = 3 ⋅ 2 = 3 ⋅ 2 = 3 ⋅ 2 = 3 ⋅ 2 ; 4) 3 3 3
4
> 0,8;
3 < 1,7321; a < 3,1464 < 3,1622 < 10 = b,
3) a = 5 − 5 ; 15 < 3,873; a > 1,127; значит, b < a ;
2)
3+ 2 2
< 3,4; значит, b < 3,4 < 4,7 < a , значит, b < a;
8− 5
112. 1)
5
> 3,9;
2
(2) 3
3( 4 5 + 4 2 ) ( 4 5 − 4 2 )( 4 5 + 4 2 )
=
3( 4 5 + 4 2 ) 5− 2
2 4
27
=
24 3 4
27 ⋅ 4 27
=
=
3( 4 5 + 4 2 )( 5 + 2 ) 3( 4 5 + 4 2 )( 5 + 2 ) = ( 4 5 + 4 2 )( 5 + 2 ) ; = 5−2 3
34
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24 3 4
34
=
24 3 ; 3