Question

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

Answer 1

∵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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