Toán Lớp 8: a) x^2(x^2+4)-x^2-4=0 b)x^4-x^3+x^2-x=0 c)4x^2-25-(2x-5)(2x+7)=0

Question

Toán Lớp 8:  a) x^2(x^2+4)-x^2-4=0 b)x^4-x^3+x^2-x=0 c)4x^2-25-(2x-5)(2x+7)=0

minhtuquynh · Answer

Giải đáp:       Lời giải và giải thích chi tiết:    a) x&sup2;(x&sup2;+4)-x&sup2;-4=(x&sup2;+4)(x&sup2;-1)=(x&sup2;+4)(x-1)(x+1)=0&rArr;x=1,x=-1   b)$x^{4}$ -x&sup3;+x&sup2;-x=0   &hArr;x&sup3;(x-1)+x(x-1)=0   &hArr;(x-1)(x&sup3;+1)=0&rArr;x=1,x=-1   c) (2x-5)(2x+5)-(2x-5)(2x+7)=0   &hArr;(2x-5)(2x+5-2x-7)=0   &hArr;(2x-5)2=0   &rArr;x=$ frac{5}{2}$

hatuanlan · Answer

Giải đáp:       Lời giải và giải thích chi tiết:     a) x&sup2;( x&sup2; + 4 ) - x&sup2; - 4 =0    &hArr; x&sup2;( x&sup2; + 4 )- ( x&sup2; + 4 )= 0   &hArr; (x&sup2; + 4 )( x&sup2; - 1 ) =0   &hArr;( x + 2)(x- 2 )(x - 1)( x+1 )   &rArr; x + 2= 0  &rArr; x = 0- 2 &rArr; x = -2   &rArr; x - 2 = 0 &rArr; x =0+2 &rArr; x = 2   &rArr; x - 1 =0  &rArr;x = 0 +1 &rArr; x = 1   &rArr; x + 1 =0 &rArr; x = 0- 1 &rArr; x = -1   Vậy x &isin; { -2 ; 2 ; 1 ; -1 }    b) x^4 - x&sup3; + x&sup2; - x = 0    &hArr; ( x^4 - x&sup3; )+ ( x&sup2; - x ) =0   &rArr;  x&sup3; ( x - 1 ) + x ( x - 1 )= 0   &rArr; ( x- 1 )( x&sup3; + x ) =0   &rArr; ( x -1 ) .x ( x&sup2; + 1) = 0   &rArr; x - 1 = 0 &rArr; x   = 0+ 1  &rArr; x = 1   &rArr; x= 0   &rArr; x&sup2; + 1 = 0 &rArr; x&sup2; = 0-1 &rArr; x&sup2; = -1 (v&ocirc; l&iacute;)   Vậy x&isin; { 1; 0}    c) 4x&sup2; - 25 - ( 2x - 5 )(2x + 7 )= 0    &rArr; ( 2x -5 )(2x + 5 ) - ( 2x - 5 )( 2x+ 7 )=0   &rArr; ( 2x - 5 ) ( 2x+ 5 - 2x - 7 )=0   &rArr; -2.(2x  - 5) =0    &rArr; 2x - 5 = 0   &rArr; 2x     = 0+ 5   &rArr; 2x     = 5   &rArr; x =  5/2   vậy x = 5/2