Question

一道数学题若代数式（2x的平方+ax-y+6)-(2b的平方-3x+5y-1)的值与字母x的取值无关,求代数式3（a的平

Answer 1

(2x^2+ax-y+6)-(2bx^2-3x+5y-1)

=2x^2-2bx+ax+3x-6y+7

=2(1-b)x^2+(a+3)x+(7-6y)

因为代数式(2x^2+ax-y+6)-(2bx^2-3x+5y-1)的值与字母x的取值无关,

所以

1-b=0,

b=1.

a+3=0,

a=-3.

3(a^2-2ab-b^2)-(4a^2+ab+b^2)

=3a^2-6ab-3b^2-4a^2-ab-b^2

=-a^2-7ab-4b^2

=-(a^2+7ab+4b^2)

=-(a+2b)^2-3ab

当a=-3,b=1时

-(a+2b)^2-3ab

=-(-1)^2+3

=-1+3

=2