对于方程a^x=x和a^(a^x)=x(a>0,a≠1)解的个数的探讨

On Solutions of a^x=x and a^(a^x)=x(a>0,a≠1)

本文讨论了两个方程a^x=x和a^(a^x)=x(a>0,a≠1)解的问题,应用高等数学中的知识给出了两个方程解的存在条件和相应的个数,纠正了一些直观的错误,通过该问题的讨论可以加深学生对高数函数知识的理解和应用.

This paper investigates solutions of two equations which often appeared in Advanced Mathematics. We discuss the conditions for solutions and number of solutions by using differential calculus, which provides a way for students to better understand functions and applications.