已知a>0,b大于0,且a+b>1,求证:(a+a/1)(b+b/1)≥4/25

题目

已知a>0,b大于0,且a+b>1,求证:(a+a/1)(b+b/1)≥4/25

答案

左式=ab+a/b+1/ab+b/a
=(a2b2+a2+1+b2)/ab
=[a2b2+(1-2ab)+1]/ab
=[(ab-1)2+1]/ab
(ab-1)2+1≥25/16,0