Question

若正数x.y满足x^2-y^2=2xy,求x-y/x+y的值

Answer 1

（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