Question

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)^2]

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

=2xy/[x^2+y^2+x^2-y^2]

=2xy/(2x^2)

=y/x

x^2-y^2=2xy

x^2-2xy-y^2=0

解出 x=(1+√2)y 或者 x=(1-√2)y

所以原式=y/x=√2-1 或者 -√2-1