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+
1个回答

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