若正数x.y满足x^2-y^2=2xy,求x-y/x+y的值RT答案是根号2-1饿,但是我需要过程

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若正数x.y满足x^2-y^2=2xy,求x-y/x+y的值RT答案是根号2-1饿,但是我需要过程
若正数x.y满足x^2-y^2=2xy,求x-y/x+y的值
RT
答案是根号2-1饿,但是我需要过程

若正数x.y满足x^2-y^2=2xy,求x-y/x+y的值RT答案是根号2-1饿,但是我需要过程
（x-y)/(x+y)
（x-y)/(x+y)=（x-y)(x+y)/(x+y)^2=(x^2-y^2)/(x^2+2xy+y^2)
=2xy/(x^2+x^2-y^2+y^2)=y/x
x^2-y^2=2xy => x/y-y/x=2
设x/y为a
所以a-1/a=2 => a^2-1=2a =>a^2-2a-1=0
a=1+√2或a=√2-1（注：√2是根号2）
=√2-1
你自己检查一下啊思路肯定对

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