Maximizing (x + y)(y + z) with Cauchy-Schwarz and AM-GM Inequalities

In this video, we tackle an exciting math problem where we find the maximum value of the expression (x + y)(y + z), subject to the condition that x² + y² + z² = 1. Using powerful mathematical tools like symmetry, the Cauchy-Schwarz inequality, and the Arithmetic Mean-Geometric Mean (AM-GM) inequality, we simplify and solve the problem step by step. Watch to learn how these techniques work together in solving optimization problems in mathematics!