解无理方程(组)通常的方法是:将方程两边乘方,化为有理方程求解,这种方法往往复杂、易错。若适当运用换元法,可降低方程的次数,使某些高次方程可解,起到化繁为简、化难为易的效果。运用换元法的关键,在于根据题目的特征(根式内外的关系)选择适当的辅助未知数.下面分别说明几类特殊无理方程(组),应如何进行换元,供参考。一、运用换元法解几类特殊的一元无理方程 (一)利用根号内、外有关项系数成比 The usual method for solving irrational equations (groups) is to transform the equations on both sides into rational equations. This method is often complex and error-prone. If the use of the substitution method is appropriate, the number of equations can be reduced, and some high-order equations can be solved, and the effect of simplifying and simplifying can be achieved. The key to applying the substitution method is to select the appropriate auxiliary unknown according to the characteristics of the topic (the relationship between the internal and external roots). The following describes the specific types of special irrational equations (groups), and how they should be exchanged for reference. First, using the substitution method to solve several types of special one-dimensional irrational equations (A) using the internal and external factors of the root number into a ratio