X²-Y²=2XY,求(X-Y)÷(X+Y)

X²-Y²=2XY,求(X-Y)÷(X+Y)
X²-Y²=2XY,求(X-Y)÷(X+Y)

X²-Y²=2XY,求(X-Y)÷(X+Y)
∵ x²-y²=2xy,
∴(x-y)(x+y)=2xy,
∴(x-y)/(x+y)
=(x-y)²/(x²-y²)
=(x²-2xy+y²)/2xy
=[x²+y²-(x²-y²)]/2xy
=2y²/2xy
=y/x
又由x²-y²=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

找点题目练练

忘了就不做好了，

拿出来初中的数学课本再看看吧

小学学的汉字忘了怎么写了
同病相怜，与君共勉