已知x(x-2)-(x²-2y)=-4,求代数式1/2(x²+y²)-xy的值

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∵x(x-2)-(x²-2y)=-4
∴x²-2x-x²+2y=-4
∴-2(x-y)=-4
∴x-y=2
1/2(x²+y²)-xy
=1/2(x²-2xy+y²)
=1/2(x-y)²
=1/2×2²
=1/2×4
=2
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