由于证明不等式的方法多种多样,因此它既是不等式这一章节的重点,也是高考命题的热点.为了提高同学们的发散思维能力及创新能力,本文特精选了一道例题,利用一题多解的形式来帮助同学们拓展解题思路.例题已知a、b∈R+,且a+b=1,求证:(a+1a)(b+b1)≥245.证明一(综合法)因为a、b∈R Because of the variety of methods used to prove inequality, it is not only the focus of the chapter on inequalities, but also the hot spot of the college entrance examination proposition. In order to improve the students’ divergent thinking ability and innovation ability, this article specially selects an example problem and uses more than one question. The solution is to help the students develop problem solving ideas. The example is known as a, b∈R+, and a+b=1. Proof: (a+1a)(b+b1)≥245. Prove one (combined method) because a, b∈R