正数x,y满足x^2-y^2=2xy,求(x-y)/(x+y)的值急.
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正数x,y满足x^2-y^2=2xy,求(x-y)/(x+y)的值急.
正数x,y满足x^2-y^2=2xy,求(x-y)/(x+y)的值
急.
正数x,y满足x^2-y^2=2xy,求(x-y)/(x+y)的值急.
(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
解:x^2-y^2=2xy
x^2-2xy+y^2-2y^2=0
(x-y)^2=2y^2
x-y=y*根号2
x=(1+根号2)y
(x,y是正数,所以,x=(1+根号2)y)
将x=(1+根号2)y代入(x-y)/(x+y)中得:
(x-y)/(x+y)=[(1+根号2)y-y]/[(1+根号2)y+y]
=(1+根号2-1)/(...
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解:x^2-y^2=2xy
x^2-2xy+y^2-2y^2=0
(x-y)^2=2y^2
x-y=y*根号2
x=(1+根号2)y
(x,y是正数,所以,x=(1+根号2)y)
将x=(1+根号2)y代入(x-y)/(x+y)中得:
(x-y)/(x+y)=[(1+根号2)y-y]/[(1+根号2)y+y]
=(1+根号2-1)/(1+根号2+1)
=根号2/2+根号2
=(根号2/2+根号2)*(2-根号2)/(2-根号2)
=根号2*(2-根号2)/2
=(2根号2-2)/2
=根号2-1
收起
视x为主元解一元二次方程；
x^2-2yx-y^2=0
x=（1＋根号2）*y(x为正，负根舍去）
(x-y)/(x+y)=(y+根号2*y-y)/(y+根号2*y+y)=根号2-1