Finding the Minimum Value of a Quadratic Expression Using AM-GM Inequality

In this video, we explore a challenging mathematical problem: finding the minimum value of the expression (a² + b² + c² + d²) / (ab + bc + cd), given that a, b, c, and d are positive. Using the Arithmetic Mean-Geometric Mean (AM-GM) Inequality, we break down the solution step-by-step, solving for the minimum value and demonstrating when equality holds. This video is ideal for students and math enthusiasts looking to deepen their understanding of inequalities and optimization techniques in algebra. Watch along and discover how we arrive at the elegant result: the square root of five minus one. Don't forget to like, share, and subscribe for more problem-solving videos!

[MrPhilippos]

Can anyone elaborate on how this version of AM GM is derived, with the t parameter? It is reminiscent of the weighted am gm, albeit not the same.