若正数x,y满足x²-y²=2xy,求（x-y)/(x+y)的值答案为√2-1_数学解答

若正数x,y满足x²-y²=2xy,求（x-y)/(x+y)的值
答案为√2-1

人气：119 ℃　时间：2020-05-02 10:42:21

解答

x²-y²=2xyx²-2xy+y²=2y²(x-y)²=2y²x-y=±y√2,x=y(1±√2),x =y(1+√2),或x =y(1-√2),y/x=1/(1+√2)=√2-1,或(-1-√2),又因为：x²-y²=2xy2x²=y²+2xy+x...