Desigualdades entre as médias geométrica e aritmética e de Cauchy-Schwarz

Abstract

This paper deals with two of the most important inequalities of Mathematics: the inequality between the geometric and arithmetic and Cauchy-Schwarz. Here several first statements for the case n = 2, after which many statements following for the general case. In these statements we use algebra elementary Euclidean geometry, geometric constructions, analytical geometry, mathematical induction, convexity of functions, Lagrange multipliers among other issues. Also selected were twenty problems that aim to give the reader a better understanding of how these inequalities can be applied in various subjects and in many ways, stimulating students' creativity in problem solving.