已知x(x-1)-(x²-y)=-6,求x²+y²/2-xy的值

题目

已知x(x-1)-(x²-y)=-6,求x²+y²/2-xy的值

答案

x(x-1)-(x²-y)=-6
整理可得：x-y=6
两边平方：（x-y）²=36
x²+y²-2xy=36
x²+y²=36+2xy
（x²+y²）/2-xy
=（36+2xy）/2-xy
=18+xy-xy
=18