（1）正数x,y满足x^2-y^2=2xy,求(x-y)/(x+y)

题目

（1）正数x,y满足x^2-y^2=2xy,求(x-y)/(x+y)
(2)已知x+y=1,求x^3+y^3+3xy的值
(最好有具体过程,好的我会追加,答出一个或两个都可以)
难道我不去做吗？一楼的你谁啊，你都懂啊

答案

（1）正数x,y满足x^2-y^2=2xy,求(x-y)/(x+y)
(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
(2)已知x+y=1,求x^3+y^3+3xy的值
x^3+y^3+3xy
=(x+y)(x^2-xy+y^2)+3xy
=1*(x^2-xy+y^2)+3xy
=x^2-xy+y^2+3xy
=(x+y)^2
=1