证明不等式的一种巧妙方法——构造辅助函数法

An Ingenious Method of Solving Inequality——the Construction of Auxiliary Function Method

中学数学中的一个难点是不等式问题,近五年的高考热点和数学竞赛中不等式所占的比例也一定程度上在增加.而函数思想已成为整个中学数学的重点和高考的热点.有些不等式采用常规方法难以解决,若能巧妙地构造函数将不等式问题转化为函数的问题,借助函数的有关性质,常能使问题获得简捷明了的解决.

Inequality teaching is a difficulty in high school mathematics teaching. There is an increase in the proportion of inequality problems in recent years＇ College Entrance Examination and a diversity of mathematics contests. The function thought has been a focus in high school mathematics teaching and College Entrance Examination. Some inequality problems can be solved in conventional ways, whereas other can be ingeniously and successfully solved by means of some related pmperties of functions after they are turned into functions.