怎么证(a+1/a)(b+1/b)大于等于25/4?

问题描述:

怎么证(a+1/a)(b+1/b)大于等于25/4?

(a-1)² ≧ 0
a² -2a + 1 ≧ 0
a² + 1 ≧ 2a
a + 1/a ≧ 2
同理:b + 1/b ≧ 2
所以
(a+1/a)(b+1/b) ≧ 2*2
(a+1/a)(b+1/b) ≧ 4