题目 :设a 0 ,b 0 ,a +b=1.求证 :(a +1a) (b + 1b)≥ 2 54 .这是一道非常优秀的不等式证明题 .它入口宽 ,思路广 ,研究它的多种证明方法可以充分体现不等式证明的常用方法 ,对数学思想方法及数学思维能力的培养均为典范作用 .下面就谈谈笔者对它的认识 .思路一　比较法是证 Title: Let a 0,b 0,a +b=1. Proof: (a +1a) (b + 1b) ≥ 2 54. This is a very good proof of inequality. It has a wide entrance, a wide range of ideas, and studies it. Many kinds of proof methods can fully reflect the common methods of inequality proof, and they are exemplary for training mathematics thinking methods and mathematics thinking ability. Let’s talk about the author’s understanding of it. The idea of ​​a comparative method is proof