已知x(x-1)-(x2-y)=-2求x2+y2-4xy的值

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已知x(x-1)-(x2-y)=-2求x2+y2-4xy的值
已知x(x-1)-(x2-y)=-2求x2+y2-4xy的值

已知x(x-1)-(x2-y)=-2求x2+y2-4xy的值
x(x-1)-(x^2-y)=-2
x^2-x-x^2+y=-2
x-y=2
x^2+y^2-4xy
=(x-y)^2-2xy
=4-2xy

x(x-1)-(x2-y)=x2-x-x2+y
=-x+y因为x(x-1)-(x2-y)=2则-x+y=2
x2+y2-4xy=x2+y2-2xy-2xy=(x-y)2-2xy=4-2xy
把y=x-2代入原式=-2x2+4x+4