1.已知正数x,y满足x2-y2=2xy,求(x-y)/(x+y)的值

题目

1.已知正数x,y满足x2-y2=2xy,求(x-y)/(x+y)的值
2.若x2+xy-2y2=0则(x2+3xy-2y2)/x2-2y2)=_________
3.先化简,后求值：(3-x)/(x-2)除以（x+2-2/(x-2)）,其中x=2√2
 

答案

1.x²-y²=（x+y）（x-y）=2xy...1
x²-y²-2xy=0
x²-2xy+y²=2y²
（x-y）²=2y².2
2/1=(x-y)/(x+y)=2y²/2xy=1/x
2.x²+xy-2y²=0
x²+3xy-2y²=2xy.1
x²+xy-2y²=0
x²-2y²=-xy.2
1/2=2xy/（-xy）=-2
3.3-x
---
x-2 3-x 3-x 3-2√2
---------- =------ = ----- = -------
2 x²-4-2 x²-6 2
x+2- ——
x-2