大家都知道,基本不等式中的等号,当且仅当诸数都相等时成立.事实上,我们遇到的要证明的绝大多数不等式的条件与结论都是关于所含字母的轮换对称式,这就预示着这些字母在解题中的地位是相同的,因此,当他们取值相同时,等号可能成立.于是,可以先猜测并验证要证明的不等式中等号成立的条件,然后,结合已知,通过拆添项、配凑等手段构造一系列基本不等式,最后通过同向不等式的运算给出证明.下面举例说明. As we all know, the equal sign in the basic inequality holds if and only if the numbers are equal. In fact, the conditions and conclusions of the vast majority of the inequalities we have to prove are rotational symmetries about the contained letters. This indicates that these letters are in the same position in the problem solving. Therefore, when they have the same value, the equal sign may be established. Therefore, you can first guess and verify the condition that the inequality that you want to prove is true, and then, Combining with known methods, a series of basic inequalities are constructed by means of adding items, matching, etc. Finally, proofs are given by operations of the same inequalities. The following examples are given.