已知x(x-1)-(x²-y)=-3,求2xy-x²+3-y²的值

题目

已知x(x-1)-(x²-y)=-3,求2xy-x²+3-y²的值

答案

∵x(x-1)-(x²-y)=-3
∴x²-x-x²+y=-3
∴x-y=3
∴2xy-x²+3-y²
=-(x²-2x+y²)+3
=-(x-y)²+3
=-(3)²+3
=-9+3
=-6