均值不等式在中学数学中有着广泛的应用.长期以来似乎有一种偏见,说均值不等式简而不精,对于那些精确程度要求较高的问题就难以奏效.为此,笔者作了一番探究,终于找出了问题的根源,并由此产生了一种新的方法,现介绍于此,以期同行指教.1 一个学生提出的问题一题多解是训练思维的好方法.一个学生在求解一个不等式问题时用了四种解法.有的失败,有的成功,有的繁冗,有的简洁,对比之下,竟有那么大的悬殊!他来问我;一四种解法,都是用的均值不等式.为什么会有如此的不同?均值不等式究竟怎样用才好?”这是一个不好回答但又很有价值的问题. Mean inequality has a wide range of applications in middle school mathematics. For a long time, there seems to be a prejudice, saying that the mean inequality is not simple and concise, and it is difficult for those problems with higher precision to be effective. For this reason, the author made some inquiry and finally found The root cause of the problem has emerged, and a new method has emerged. Now it is introduced here, in the hope of peer advice. 1 A student’s question is a good way to train his thinking. A student is solving an inequality problem. Four kinds of solutions were used. Some failed, some succeeded, some were tedious, and some were succinct. In contrast, there was so much disparity! He came to ask me; one of the four solutions is a mean inequality. Why is there such a difference? How can the mean inequality be used?” This is a question that is not easy to answer but valuable.