Abstract: Mean inequality is a common method to solve the maximum problem, but it is also an error-prone method. A little carelessness will lead to mistakes that are not easy to find. Here are two examples to illustrate. Example 1 Let the base area of a cuboid be 4 and the diagonal length be 4, and try to find the maximum lateral area of the cuboid. Wrong solution 1 as shown in figure 1. Let the length, width and height of a cuboid be x, y and z respectively, and lateral area be s. According to the meaning of the question, {xy = 4, ① x ~ 2+y ~ 2+z ~ 2 = 16. ② s = 2 (x+y) z consider S ~ 2 = 4 (x+y).