= 2 a ⋅ 3 a − 2 a ⋅ 2 b + 3 a ⋅ b − 2 b ⋅ b = 6a − ab − 2b;
з) (4 x − 2 x )( x − 2 x ) = = 4 x ⋅ x − 4 x ⋅ 2x − x ⋅ 2x + 2x ⋅ 2x = 6x − 5x 2.
488. а) (1 − x )(1 + x + x) = 13 − ( x ) 3 = 1 − x x ; б) ( a + 2)(a − 2 a + 4) = ( a ) 3 + 23 = a a + 8; в) ( m − n )(m + n + mn ) = ( m ) 3 − ( n ) 3 = m m − n n ; г) ( x + y )( x 2 + y − x y ) = x 3 + ( y ) 3 = x 3 + y y . 489. a) ( 6 + 4 2 ) 2 = (2 + 2 ) 2 ;
6 + 4 2 = 4 + 2 ⋅ 2 2 + ( 2 )2 ;
6 + 4 2 = 6 + 4 2 , тождество доказано;
б) ( 8 3 + 19 ) 2 = ( 3 + 4) 2 ;
8 3 + 19 = ( 3 ) 2 + 2 ⋅ 4 3 + 16;
8 3 + 19 = 8 3 + 19, тождество доказано.
490. а) Подставим x = 1 + 5 : x 2 − 6 = (1 + 5 ) 2 − 6 = 1 + 2 5 + ( 5 ) 2 − 6 = = 2 5;
б) Подставим x = 3 − 3 : x 2 − 6 x = (3 − 3 ) 2 − 6(3 − 3 ) = = 9 − 2 ⋅ 3 3 + ( 3 ) 2 − 6 ⋅ 3 + 6 3 = −6;
в) Подставим x = 2 + 3 : x 2 − 4 x + 3 = (2 + 3 ) 2 − 4(2 + 3 ) + 3 = = 4 + 2 ⋅ 2 ⋅ 3 + ( 3 ) 2 − 8 − 4 3 + 3 = 4 + 4 3 + 3 − 8 − 4 3 + 3 = 2;
г) Подставим x =
3+ 2 3+ 2 2 3+ 2 : x 2 − 3x + 5 = ( ) − 3( )+5= 2 2 2
=
9 + 3 ⋅ 2 2 + ( 2 )2 9 + 3 2 11 + 6 2 9 + 3 2 − +5= − +5= 4 2 4 2
=
11 + 6 2 − 18 − 6 2 + 20 13 = = 3,25. 4 4
491*. 1) ( 7 + 4 3 + 7 − 4 3 ) 2 =
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