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--- pow:problem6s25 [2025/04/27 15:56]
mazur created
+++ pow:problem6s25 [2025/05/01 14:51] (current)
mazur
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+<box 85% round orange| Problem 6 (due Monday, April 28 )>
+Prove that if $a,b,c$ are positive numbers such that $abc=1$ then
+\[ \frac{1}{\sqrt{1+2024a}}+\frac{1}{\sqrt{1+2024b}}+\frac{1}{\sqrt{1+2024c}}\geq\frac{1}{15}.\]
+</box>
+We received a solution from  Emily (Qingyue) Liu, Josiah Moltz, and Andrew Zhou (a high school senior from Cincinnati, OH).
+Andrew's solution is based on a certain general result in elementary inequalities called the N-1 Equal Value Principle. The solution from Josiah Moltz is perhaps the simplest of all the solutions we have.
+For details and other solutions see the following link {{:pow:2025sproblem6.pdf|Solution}}.