若正数x,y满足x²-y²=2xy,求（x-y)/(x+y)的值答案为√2-1

若正数x,y满足x²-y²=2xy,求（x-y)/(x+y)的值答案为√2-1
若正数x,y满足x²-y²=2xy,求（x-y)/(x+y)的值
答案为√2-1

若正数x,y满足x²-y²=2xy,求（x-y)/(x+y)的值答案为√2-1

x²-y²=2xy
x²-2xy+y²=2y²
(x-y)²=2y²
x-y=±y√2, x=y(1±√2),
x =y(1+√2),或x =y(1-√2),
y/x=1/(1+√2)=√2-1,或(-1-√2),
又因为：x²-y²=2xy
2x²=y²+2xy+x²
(x+y)²=2x²
x+y=±x√2, y=x(-1±√2), y =x(-1+√2),或y =x(-1-√2),
y/x=-1+√2 ,或(-1-√2).
由此可见y/x 的值有两种可能.即y/x=√2-1,或y/x=-1-√2
又因为(x-y)/(x+y)=[1-y/x]/[1+y/x]
所以它的值有两种可能
（1）把y/x=√2-1代入,得(x-y)/(x+y)=√2-1
（2）把y/x=-1-√2代入,得(x-y)/(x+y)=-√2-1