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不等式有两个显著的特点:一是其应用的广泛性,不等式与各个数学分支都有密切的联系,数学的基本结果往往是一些不等式而不是等式;二是其方法的高度技巧性,被称为“创造性的艺术”.这就不难理解,为什么不等式成了各种数学考试,特别是各类数学竞赛的热门试题.笔者曾总结出50种有代表性的证明不等式的常用方法,其中大多数是在各种数学竞赛中常用的方法和技巧.证明不等式的关键之一就是要熟练掌握各种变形的技巧.下面以1986年第20届全苏数学奥林匹克题为例.
Inequalities have two salient features: First, the wide range of applications, inequalities and various mathematical branches are closely linked to the basic results of mathematics are often some inequalities rather than equations; the second is its highly technical skills, was Called “creative art.” It is not hard to understand why Inequality has become a hot topic in various math exams, especially in all kinds of math contests. The author has summed up 50 representative commonly used methods to prove inequalities , Most of which are methods and techniques commonly used in various mathematical competitions One of the keys to demonstrating inequalities is to master a variety of techniques for deformations The following is an example of the 20th Olympiad for All-Soviet Mathematical Olympiad in 1986.