Question

若4x^2+4xy+2y^2-6y+9=0,试求（x^2+2y^2+3）（x^2+2y^2-3）-（x-2y）^2（x+

Answer 1

4x^2+4xy+2y^2-6y+9=0

(2x+y)²+(y-3)²=0

则：

2x+y=0

y-3=0

解得：

x=-3/2；y=3

（x^2+2y^2+3）（x^2+2y^2-3）-（x-2y）^2（x+2y）^2

=(x²+2y²)²-9-(x²-4y²)²

=(x²+2y²+x²-4y²)(x²+2y²-x²+4y²)-9

=6y²(2x²-2y²)-9

=12(x+y)(x-y)-9

=12×3/2×(-9/2)-9

=-81-9

=-90