若x（y-1)-y(x-1)=4,则(x²+y²)/2-xy=

来源：学生作业帮助网编辑：作业帮时间：2024/10/03 04:55:37

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若x（y-1)-y(x-1)=4,则(x²+y²)/2-xy=
若x（y-1)-y(x-1)=4,则(x²+y²)/2-xy=

若x（y-1)-y(x-1)=4,则(x²+y²)/2-xy=
解
x(y-1)-y(x-1)=4
即xy-x-xy+y=4
∴y-x=4
两边平方得
y²-2xy+x²=16
∴x²+y²=16+2xy
∴(x²+y²)/2-xy
=(16+2xy)/2-xy
=8+xy-xy
=8

将x(y-1)-y(x-1)=4展开得到：
xy-x-xy+y=4
所以-x+y=4
即x-y=-4
而(x²+y²)/2-xy
=(x²-2xy+y²)/2
=(x-y)²/2
=(-4)²/2
=8

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