Maximizing a + 1/a Using the Cauchy-Schwarz Inequality

In this video, we solve a fascinating mathematical optimization problem involving the Cauchy-Schwarz inequality. Starting with the conditions \(a + b + c + d = 10\) and \(\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} = 10\), we find the maximum value of \(a + \frac{1}{a}\). Watch as we employ symmetry, algebraic techniques, and the power of inequalities to reveal that the maximum occurs when \((a, b, c, d)\) satisfies unique properties. Perfect for students preparing for math competitions or those passionate about problem-solving!

[@ronbannon]

Always a pleasure to see the problems you post. Thanks for sharing.

[@chanlyelee]

Thanks. 🙏 👍

[@gregevgeni1864]

Nice solution!
Thanks for sharing!

[@chanlyelee]

Thanks 🙏👍