Mathematical inequalities play a pivotal role in problem-solving within mathematical olympiads. This paper explores diverse techniques for proving inequalities, emphasizing their practical application in competitive settings. By presenting classical and advanced methods such as AM-GM, Cauchy-Schwarz, and Jensen's inequalities, the paper provides a comprehensive guide for students preparing for olympiads. A systematic approach to understanding and solving inequality problems is discussed, alongside illustrative examples.

Mathematical Inequalities, Olympiad Problem-Solving, AM-GM Inequality

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