已知x,y满足x^2+y^2+5/4=2x+y,求 xy/x+y的值
1个回答
2010-02-10
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x^2+y^2+5/4=2x+y,
==>(x^2-2x+1)+(y^2-y+1/4)=0
==>(x-1)^2+(y-1/2)^2=0
则x-1=0
y-1/2=0
x=1,y=1/2
则xy/(x+y)
=1*1/2/(1+1/2)
=1/3
==>(x^2-2x+1)+(y^2-y+1/4)=0
==>(x-1)^2+(y-1/2)^2=0
则x-1=0
y-1/2=0
x=1,y=1/2
则xy/(x+y)
=1*1/2/(1+1/2)
=1/3
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