若正数x.y满足x^2-y^2=2xy,求x-y/x+y的值
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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
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](/uploads/image/z/18899957-29-7.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%BC)
(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
(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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