ab>0.(a+b)(1/a+1/b)大于等于多少?

题目

ab>0.(a+b)(1/a+1/b)大于等于多少?

答案

ab>0.
(a-b)²>=0
a²+b²>=2ab
(a+b)(1/a+1/b)
=(a+b)(a+b)/ab
=(a²+b²+2ab)/ab>=4ab/ab=4
所以,ab>0.有:(a+b)(1/a+1/b)>=4