均值不等式在中学数学教学中有着广泛的应用．但有人说，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凑效．于是如柯西不等式等一些超纲内容又被引进课堂，加重了学生的负担．本文着意介绍一种新的方法，希望能有助于改变这一局面．一、一个学生提出的问题... Mean inequality has a wide range of applications in mathematics teaching in middle school. However, it is said that the mean inequality is not simple but it is difficult to work for those problems with higher precision. Therefore, some super-level contents such as Cauchy inequality have been introduced into the classroom, which has increased the burden on students. This article aims to introduce a new method, hoping to help change this situation. First, a student raises questions...