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](/uploads/image/z/10368108-36-8.jpg?t=%E8%8B%A5%E6%AD%A3%E6%95%B0x.y%E6%BB%A1%E8%B6%B3x%5E2-y%5E2%3D2xy%2C%E6%B1%82x-y%2Fx%2By%E7%9A%84%E5%80%BCRT%E7%AD%94%E6%A1%88%E6%98%AF%E6%A0%B9%E5%8F%B72-1%E9%A5%BF%2C%E4%BD%86%E6%98%AF%E6%88%91%E9%9C%80%E8%A6%81%E8%BF%87%E7%A8%8B)
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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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