MathDB
Inequality involving GM, QM, HM

Source: Tuymaada 2013, Day 1, Problem 3 Juniors

July 20, 2013
inequalitiesinequalities proposed

Problem Statement

For every positive real numbers aa and bb prove the inequality ab≤13a2+b22+2321a+1b.\displaystyle \sqrt{ab} \leq \dfrac{1}{3} \sqrt{\dfrac{a^2+b^2}{2}}+\dfrac{2}{3} \dfrac{2}{\dfrac{1}{a}+\dfrac{1}{b}}.
A. Khabrov
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