正数x,y满足x2－y2＝2xy,求(x-y)/(X+Y）的值

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正数x,y满足x2－y2＝2xy,求(x-y)/(X+Y）的值
正数x,y满足x2－y2＝2xy,求(x-y)/(X+Y）的值

正数x,y满足x2－y2＝2xy,求(x-y)/(X+Y）的值
x2-2xy+Y2－2*y2=0
(X-Y)²-2Y²=0
X=(1-根号2）因为为正数,所以不合题意,舍去
X=(1+根号2）Y
(x-y)/(X+Y)=根号2-1

x^2 - y^2 = 2xy
x/y - y/x = 2
(x/y - y/x)^2 = 4
(x/y + y/x)^2 = 8
x/y+y/x = 2*2^(1/2)
(x-y)/(x+y) = (x-y)^2/(x^2-y^2) = (x^2 - 2xy + y^2)/(2xy)
= (1/2)(x/y +y/x) - 1
=2^(1/2) -1

正数x,y满足x²-y²＝2xy,求(x-y)/(X+Y）的值
将方程x²-y²=2xy的两边同除以xy得：(x/y)-(y/x)=2............(1)
令x/y=u，则y/x=1/u，代入(1) 式得u-(1/u)=2，即有u²-2u-1=0，故u=(2+√8)/2=1+√2
于是得(x-y)/(x+y)=[...

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根号2-1

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