正数xy满足x2-y2=2xy,求x+y分之x-y的值2是平方,

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正数xy满足x2-y2=2xy,求x+y分之x-y的值2是平方,
正数xy满足x2-y2=2xy,求x+y分之x-y的值
2是平方,

正数xy满足x2-y2=2xy,求x+y分之x-y的值2是平方,
x^2-y^2=2xy,得x/y-y/x=2,即（y/x)^2+2(y/x)-1=0∴y/x=-1+√2或y/x=-1-√2(舍去,因为x,y都是正数).即（x-y)/(x+y)=√2-1

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+√2a或=-1-√2(舍去，因为x，y都是正数)
=√2-1

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