已知x(x-1)-(x²-y)=-6,求x²+y²/2-xy的值

已知x(x-1)-(x²-y)=-6,求x²+y²/2-xy的值
已知x(x-1)-(x²-y)=-6,求x²+y²/2-xy的值

已知x(x-1)-(x²-y)=-6,求x²+y²/2-xy的值
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

∵ x(x-1)-(x²-y)=-6
∴x-y=6
∴x²-2xy+y²=36
∴(x²+y²)/2-xy=18

已知得：x-y=6
∴x²+y²-2xy=(x-y）²=6²=36

x(x-1)-(x²-y)=x²-x-x²+y=y-x= -6
x²+y²/2-xy=1/2(y-x)²=1/2 ×（-6）= -3