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

正数x,y满足x²-y²=2xy.求x-y/x+y的值
x²-y²=2xy
x²-2xy+y²=2y²
（x-y)^2=2y^2
(x-y-√2y)(x-y+√2y)=0
x1=(1+√2）y
x2=(1-√2）y(舍去）
x-y/x+y
=√2y/(2+√2）y
=√2*(2-√2）/2

答：
x²-y²=xy
x²-yx-y²=0
解得：
x=(y±√5y)/2
因为：x和y都是正数
所以：x=(1+√5)y/2
所以：x/y=(1+√5)/2
(x-y)/(x+y)
=(x/y-1)/(x/y+1)
=[(1+√5)/2-1]/[(1+√5)/2+1]

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答：
x²-y²=xy
x²-yx-y²=0
解得：
x=(y±√5y)/2
因为：x和y都是正数
所以：x=(1+√5)y/2
所以：x/y=(1+√5)/2
(x-y)/(x+y)
=(x/y-1)/(x/y+1)
=[(1+√5)/2-1]/[(1+√5)/2+1]
=(√5-1)/(√5+3)
=(√5-1)(3-√5)/4
=√5-2

收起

• x^2-y^2=2xy

• x^2-2xy+y^2-2y^2=0

• (x-y)^2-2y^2=0

• x-y-2^0.5y=0

• x=1+根2*y

• x-y/x+y=根2-1