正数x,y满足x^2-y^2=2xy,求(x-y)除以(x+y)的值.

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正数x,y满足x^2-y^2=2xy,求(x-y)除以(x+y)的值.正数x,y满足x^2-y^2=2xy,求(x-y)除以(x+y)的值.正数x,y满足x^2-y^2=2xy,求(x-y)除以(x+

正数x,y满足x^2-y^2=2xy,求(x-y)除以(x+y)的值.
正数x,y满足x^2-y^2=2xy,求(x-y)除以(x+y)的值.

正数x,y满足x^2-y^2=2xy,求(x-y)除以(x+y)的值.
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 所以原式=√2-1 (另一个舍去,因为X,Y都是正数)