Question

已知x，y满足x的平方+y的平方+4/5=2x+y，求代数式xy/x+y的值

Answer 1

x²+y²+5/4=2x+y
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
(x+y)/xy
=(1+1/2)/(1*1/2)
=(3/2)/(1/2)
=3

Answer 2

解：
x²+y²+5/4=2x+y
x²+y²+5/4-2x-y=0
x²-2x+1+y²-y+1/4=0
(x-1)²+(y-1/2)²=0
所以x-1=0 y-1/2=0
得x=1 ,y=1/2
xy/（x+y）=1×1/2/（1+1/2）=1/3