已知x(x-1)-(x²-y)=-6,求x²+y²/2-xy的值
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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