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无理方程在初中代数课本中仅仅介绍了一般解法(即方程两边同时平方)和换元法两种。但在实际解无理方程时,单用这两种方法往往无济于事,或是繁琐冗长。近两年来,各地出版的中学数学杂志和资料中,介绍了用三角变换解一类无理方程的方法。它拓广了解题的思路,沟通了各科知识的联系,也培养了学生灵活运用知识的能力。遗憾的是它还不能为初中学生所用。为了“抓好基础”,有必要对这类无理方程,寻求适合中学生所能用的解法。本文试图通过对这类无理方程的非三角变换解法,来说明加强初中基础课教学,对“培养能力,发展智力”的重要意义。
The irrational equation in the junior high school algebra textbook only introduces the general solution (that is, the equation on both sides of the same square) and the two-way method. However, in the practical solution of irrational equations, the use of these two methods alone is often unhelpful or cumbersome. In the past two years, in middle school mathematics magazines and materials published throughout the country, methods for solving a class of irrational equations using trigonometric transformation have been introduced. It broadens the train of thoughts of the questions, communicates the links of various subjects, and cultivates the students’ abilities to use knowledge flexibly. Unfortunately, it cannot be used by junior high school students. In order to “grasp the foundation,” it is necessary to seek solutions suitable for middle school students for such irrational equations. This paper attempts to illustrate the importance of strengthening the teaching of junior high school basic courses by means of the non-triangular transformation of such irrational equations.