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解无理方程是初中数学的重要问题之一,初中课本中仅仅介绍了两种解法,即方程两边同次乘方法和换元法。但是,有时会遇到一些复杂的无理方程,若采用这两种方法来解,往往繁琐冗长,易出差错。因此,探究无理方程的其他解法还是一项十分有益的工作。这里主要介绍几种用高中的知识解无理方程的方法,供教学中参考。一、函数性质法我们知道,无理方程中含有一些无理函数。如果注意到这些函数的性质(比如定义
Solving irrational equations is one of the important problems in junior high school mathematics. In junior high school textbooks, only two kinds of solutions are introduced, namely, the same side multiplication method and the equivalence method. However, some complicated and unreasonable equations are sometimes encountered. If these two methods are used to solve, it is often cumbersome and lengthy, and it is easy to go wrong. Therefore, exploring other solutions to the irrational equation is still a very useful job. Here is a brief introduction of several ways to solve unreasonable equations using high school knowledge for reference in teaching. First, the function of the law We know that irrational equation contains some irrational function. If you notice the nature of these functions (such as the definition