Question

设a>b>0,a²+b²=10/3ab,求(a+b)/(a-b)

Answer 1

解答如下：
a²+b²=10/3ab
两边同加上2ab得，（a + b）² = 16/3ab
两边同减去2ab得，（a - b）² = 4/3ab
两式子比一下得，（a + b）²/（a - b）² = 4
因为a ＞ b ＞ 0
所以(a+b)/(a-b) = 2

Answer 2

a²+b²=10/3ab
两边同除以ab,得
a/b+b/a=10/3=3+1/3
所以
a/b=3,或a/b=1/3
(a+b)/(a-b)
=(a/b+1)/(a/b-1)
=(3+1)/(3-1)
=2
或
(a+b)/(a-b)
=(a/b+1)/(a/b-1)
=(1/3+1)/(1/3-1)
=-2