pow:problem6s25 [Department of Mathematics and Statistics, Binghamton University]

Problem 6 (due Monday, April 28 )

Prove that if $a,b,c$ are positive numbers such that $abc=1$ then

$\frac{1}{\sqrt{1+2024a}}+\frac{1}{\sqrt{1+2024b}}+\frac{1}{\sqrt{1+2024c}}\geq\frac{1}{15}.$

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 Solution.

User Tools

Site Tools

−Sidebar

Page Tools