已知x,y满足x^2+y^2-2x-y+5/4=0 - 知识问答

已知x,y满足x^2+y^2-2x-y+5/4=0,求代数式xy(x+y)的值

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解
x²+y²-2x+y+5/4=0
(x²-2x+1)+(y²+y+1/4)=0
(x-1)²+(y+1/2)²=0
∴x-1=0,y+1/2=0
∴x=1,y=-1/2
∴xy(x+y)
=1×(-1/2)(1-1/2)
=-1/2×(1/2)
=-1/4

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