The Arithmetic Mean - Geometric Mean - Harmonic Mean: Inequalities and a Spectrum of Applications

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. "Classroom" is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science. The Arithmetic Mean - Geometric Mean - Harmonic Mean inequality, AM-GM-HM inequality in short, is one of the fundamental inequalities in Algebra, and it is used extensively in olympiad mathematics to solve many problems. The aim of this article is to acquaint students with the inequality, its proof and various applications.