100/(x-y)+100/(x+y)=100/y 怎么解

题目

100/(x-y)+100/(x+y)=100/y 怎么解
100/(x-y)+100/(x+y)=100/y
怎么解出 x=(1+根号2)y

答案

100/(x-y)+100/(x+y)=100/y
1/(x-y)+1/(x+y)=1/y
通分
(x+y+x-y)/(x+y)(x-y)=1/y
2x/(x+y)(x-y)=1/y
对角相乘
2xy=(x+y)(x-y)=x^2-y^2
x^2-2xy-y^2=0
把y看成已知
则x^2-2xy+y^2=2y^2
(x-y)^2=2y^2=(±√2y)^2
x-y=±√2y
x=y±√2y=(1±√2)y