The so-called direct method is to solve directly with basic inequalities. The specific process of solving the problem is as follows: this is the simplest and most direct solution, of course, this solution is only suitable for solving some simple basic inequalities. This is an inevitable topic.

Method two? eliminate

This exclusion method can be said to be one of the most common general solutions to this kind of problems. The method is easy to understand and master, but we should pay attention to the range of new yuan or new variables in the process of solving problems. The specific problem solving process is as follows:

This solution embodies the transformation of multivariate problems into univariate problems, and finally its maximum value is transformed into the maximum value of univariate functions. It is a strategy to solve problems from the perspective of function.

Method three? Discrimination method of roots

As for the root discrimination method, as long as there is a relationship between two variables and the problem of finding the maximum value of the algebraic expression of another two variables, this method can be tried. Of course, there must be an applicable condition. This condition is to get a quadratic equation of one variable about another parameter by eliminating one parameter after substitution. Otherwise, it cannot be used.

The specific problem solving process is as follows:

Method 4? Replacement method (including triangular exchange)

Method of substitution is widely used in college entrance examination mathematics, and naturally occupies a place in finding the maximum inequality. Therefore, there are alternative methods to solve this problem, and the specific process is as follows:

Students, you see, the triangle exchange method is so wonderful, giving people another feeling of thinking about the world!