A Study on Cauchy-Schwarz Inequality and its Various Applications in Solving Inequalities with Exploring its Geometric Interpretation and Related Inequalities

The Cauchy-Schwarz inequality is one of the most fundamental inequalities in the world of mathematics with its powerful ability for solving complex inequality problems. This research article illustrates the deep study of Cauchy-Schwarz inequality with its various proofs (algebraic and geometric) including its applications in the mathematical world of inequalities. The paper will to deepen our knowledge and understanding of this inequality exploring its implications. The article includes other related inequalities like Triangle Inequality, Minkowski Inequality, and Hölder’s Inequality