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在数学竞赛中,常常遇到含有x+y=A型条件的问题,我们设用x=A/2+t,y=A/2-t来代换参与运算——均值代换。“均值代换法”是数学解题中的一种常用有效解题方法,既可揭示化难为易的思维规律,又能体现以退求进的解题策略,恰当施行“均值代换”,可把内容与形式、方法与知识结合起来思考,使我们的解题思路更加灵活,解题过程更加完美,收到事半功倍之效应。本文试就以下几个方面的应用举例,来领略其风采。1 求值
In mathematics competitions, we often encounter problems with x+y=A conditions. Let us substitute x=A/2+t,y=A/2-t to participate in the operation—mean substitution. The “mean substitution method” is a commonly used effective problem-solving method in mathematics problem solving. It can not only reveal the law of thinking that is difficult to be changed, but also embody the problem-solving strategy of retreat and progress, and properly implement “mean substitution”. We can combine content and form, methods and knowledge to think and make our problem-solving ideas more flexible, the problem-solving process more perfect, and the effect of getting twice the results with half the effort. This article tries to appraise its elegance on the following aspects of application examples. 1 Evaluation