解无理方程中学课本主要讲述“两边平方法”与简单的“换元法”,实际上很多无理方程用这些常规方法不易解出,因此必须根据不同形式的无理方程寻求其特殊解法。现举例介绍解无理方程的十一种特殊方法,供教学参考。 一、利用定义域 例1 解方程(2x—3)~(1/2)-(4—5x)(1/2)=6x Solutions for irrational equations Middle school textbooks mainly describe the “two-sided method” and the simple “substitution method”. In fact, many irrational equations are not easily solved by these conventional methods. Therefore, special solutions must be sought based on different forms of irrational equations. An example of eleven special methods for solving irrational equations is provided for teaching reference. First, the use of the definition of domain Example 1 Solution equation (2x - 3) ~ (1/2) - (4 - 5x) (1/2) = 6x