The Studies Of Cauchy-inequality In The Application Of The High School Olympiad

Cauchy-inequality is a very important inequality in the field of elementary mathematics. After the new curriculum reforming, Cauchy inequality was incorporated into the content of the mathematics courses that makes the content become a hot issue in mathematics competition once again. Only we can use of this inequality well, many complex problems can be solved easily. For example, its advantage is obvious during the process to prove inequality, seek the most value of the function and solve triangle related problems.This thesis mainly studies the discrete form of Cauchy-inequality in the application of the high school Olympiad. This paper is divided into four chapters, the original history and development of IMO and CMO is expounded on the start. The second chapter describes the forms of Cauchy-inequality, there are more than twenty presentative and tricky methods of proving the inequality. This article selects the seven representative ones that cam make the high school students more conducive to understand. And the deformation of Cauchy inequality and promote in-depth exploration has been proved that this can be extended the application scope of Cauchy inequality. And some details about the relationship between the Cauchy inequality with n inequality chain also are represented here. The third chapter mainly aimed at the problems of Cauchy inequality in IMO and CMO and the methods and techniques of problem-solving are analyzed and summarized. The fourth chapter is about a few of problems of Cauchy inequality based on the research achievements of the previous chapter for the reader to appreciate. The value of this thesis is the study of the related knowledge of Cauchy inequality systematically and detailedly and the explore in math competition, which can provide reference to that.