Toán Lớp 8: tinh gia tri cua bieu thuc: a)x^2+4x+4 tai x=98;b)x^3+3x^2+3x+1tai x=99 chung minh cac dang thuc sau: a) (a-b)^3=-(b-a)^3 b) (-a-b)^2=9

Question

Toán Lớp 8:  tinh gia tri cua bieu thuc: a)x^2+4x+4 tai x=98;b)x^3+3x^2+3x+1tai x=99 chung minh cac dang thuc sau: a) (a-b)^3=-(b-a)^3 b) (-a-b)^2=9a+b)^2 giai giúp minh voi a

diepbich93 · Answer

y10000   a )   x&sup2; + 4x + 4   = x&sup2; + 2 . x .2 + 2&sup2;   = ( x + 2 )&sup2;   $ text{Thay x = 98 v&agrave;o biểu thức ta c&oacute; :}$       ( 98 + 2 )&sup2;   = 100&sup2;   = 10000   b )   x&sup3; + 3x&sup2; + 3x + 1   = x&sup3; + 3 . x&sup2; . 1 + 3 . x . 1&sup2; + 1&sup3;   = ( x + 1 )&sup3;   $ text{Thay x = 99 v&agrave;o biểu thức ta c&oacute; :}$       ( 99 + 1 )&sup3;   = 100&sup3;   = 1000000   c )   ( a - b )&sup3; = - ( b - a )&sup3;   $ text{Vế phải :}$   - ( b - a )&sup3;   = - ( b&sup3; - 3b&sup2;a + 3ba&sup2; - a&sup3; )   = -b&sup3; + 3ab&sup2; - 3a&sup2;b + a&sup3;   = a&sup3; - 3a&sup2;b + 3ab&sup3; - b&sup3;   = ( a - b )&sup3;        $ text{(đpcm)}$   d )    ( -a - b)&sup2; = ( a + b )&sup2;   $ text{Vế tr&aacute;i :}$   ( -a - b )&sup2;   = a&sup2; - 2 . ( -a ) . b + b&sup2;   = a&sup2; + 2ab + b&sup2;   = ( a + b )&sup2;       $ text{(đpcm)}$

ngoclanquynh · Answer

$  $   B&agrave;i 1.   a,   x^2  +4x+4   = x^2 + 2 . x . 2 +2^2   = (x+2)^2   Thay x=98 v&agrave;o BT ta được :   = (98+2)^2   = 100^2   = 100 00   Vậy x^2 +4x+4=100 00 khi x=98   b,   x^3 +3x^2 +3x+1   = x^3 + 3 . x^2 . 1+3 . x.  1^2 +1^3   =(x+1)^3   Thay x=99 v&agrave;o BT ta được :   =(99+1)^3   = 100^3   = 100 000   Vậy x^3+3x^2 +3x+1=100 000 khi x=99   $  $   B&agrave;i 2.   a,   X&eacute;t vế tr&aacute;i :   = (-b +a)^3   = [- (b-a)]^3   = - (b-a)^3 (Bằng vế phải)   -> Đpcm   b,   X&eacute;t vế tr&aacute;i :   = [- (a+b)]^2   = (a+b)^2 (Bằng vế phải)   -> Đpcm