若多项式3x^2+ary-2y^2+1与2bx^2-3xy+y^2的差值与x的取值无关,求代数式2（a^2-2ab+b^2）-3(b^2-a^2)

Question

若多项式3x^2+ary-2y^2+1与2bx^2-3xy+y^2的差值与x的取值无关,求代数式2（a^2-2ab+b^2）-3(b^2-a^2)

Answer 1

3x^2+axy-2y^2+1与2bx^2-3xy+y^2的差值与x的取值无关
(3x^2+ary-2y^2+1) - (2bx^2-3xy+y^2)
=(3-2b)x^2+(a+3)xy+(-2-1)y^2+1
3-2b=0；a+3=0
a=-3,b=3/2
2（a^2-2ab+b^2）-3(b^2-a^2)
=2a^2-4ab+2b^2-3b^2+3a^2
=5a^2-4ab-b^2
=5*(-3)^2-4*(-3)*3/2-(3/2)^2
=45+18-9/4
=243/4