最值问题是中学数学的一个基本问题,解决的方法很多,如分析法(单调性法)、判别式法、平均值不等式法、数形结合法、导数法等.对称性是数学的重要特征,几何、代数中充满着各种类型的对称美.充分挖掘问题中的对称性,常常能够启迪思维,启发人们探索解题思路,发现巧妙解法.下面通过 The problem of the maximum value is a basic problem in middle school mathematics, and there are many methods to solve it, such as analytical methods (monotonicity method), discriminant methods, mean inequality methods, number-form combination method, derivative method, etc. Symmetry is an important feature of mathematics. Geometry and algebra are filled with various types of symmetry. Excavating the symmetry in the problem can often inspire thinking, inspire people to explore problem solving ideas, and discover clever solutions.