已知:5x2-4xy+y2-2x+1=0,求(x-y)2007的值______.
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已知:5x2-4xy+y2-2x+1=0,求(x-y)2007的值______.
![已知:5x2-4xy+y2-2x+1=0,求(x-y)2007的值______.](/uploads/image/z/15672084-60-4.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9A5x2-4xy%2By2-2x%2B1%3D0%EF%BC%8C%E6%B1%82%EF%BC%88x-y%EF%BC%892007%E7%9A%84%E5%80%BC______%EF%BC%8E)
∵5x2-4xy+y2-2x+1=0,
∴4x2-4xy+y2-2x+1+x2=0,
∴(2x-y)2+(x-1)2=0,
∴2x-y=0且x-1=0,
∴x=1,y=2,
∴(x-y)2007=-1.
故答案为:-1.
∴4x2-4xy+y2-2x+1+x2=0,
∴(2x-y)2+(x-1)2=0,
∴2x-y=0且x-1=0,
∴x=1,y=2,
∴(x-y)2007=-1.
故答案为:-1.
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