正数x,y满足x^2-y^2=2xy,则(x-y)/(x+y)=???

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热心网友 时间：1小时前

首先
有x^2-y^2=2xy
(x+y)^2=x^2+2xy+y^2=2x^2
x^2-y^2=(x-y)(x+y)=2xy
而（x^2-y^2）/(x+y)^2=(x-y)/(x+y)=y/x
考虑到正数x,y满足x^2-y^2=2xy
同除以xy：
x/y-y/x=2
所以y/x=根号2-1
所以(x-y)/(x+y)=根号2-1

热心网友 时间：1小时前

x^2+y^2=√(x^2-y^2)^2+4x^2y^2=√(2xy)^2+4x^2y^2=2√2xy
(x-y)^2=x^2+y^2-2xy=(2√2-2)xy
(x-y)/(x+y)=(x-y)^2/[(x+y)(x-y)]=(2√2-2)xy/2xy=(2√2-2)/2=√2-1

热心网友 时间：1小时前

（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
所以原式=√2-1

热心网友 时间：1小时前

x²-y²=2xy
x²-y²-2xy=0
(x-y)²=2y²又∵x,y是正数
(x-y)=√2y
(x-y)/(x+y)=√2/(√2+2)=√2-1