Finding the Minimum Value of 2x + y: Optimization with AM-GM Inequality

In this video, we explore a challenging optimization problem involving the Arithmetic Mean-Geometric Mean (AM-GM) inequality. The goal is to find the minimum value of the expression 2x + y given the equation xy²(x + y) = 9. We approach the problem step by step, using substitution, algebraic manipulation, and the AM-GM inequality to derive the solution. Along the way, we confirm the result through two methods, ensuring that the minimum value is 2√3.

If you’re interested in optimization, inequalities, or solving mathematical problems, this video will provide a clear and insightful explanation.

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[hamdamoverali]

Thank you very much. Your video really helped me finally understand how to apply AM-GM inequality. Thank you very, very much

[gregevgeni]

Very high technique in the first solution but the second solution is elegant! Thanks