Question

已知x。y满足x的平方+y的平方+4分之5=2x+y，求x+y分之xy的值

请告诉我详细过程

Answer 1

x^2+y^2+5/4=2x+y
(x-1)^2+(y-1/2)^2=0
x=1,y=1/2
xy/(x+y)=1*(1/2)/(1+1/2)=1/3
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Answer 2

由x²+y²+5/4=2x+y
得x²-2x+1+y²-y+1/4=0
即(x-1)²+(y-1/2)²=0
又(x-1)²≥0,(y-1/2)²≥0
∴(x-1)²=0,(y-1/2)²=0
即x=1,y=1/2
xy/(x+y)=1/3

Answer 3

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
=> x-1=0,y-1/2=0
=>x=1,y=1/2
=>xy/(x+y) = 1/3