MathDB

A1

Part of 2008 Balkan MO Shortlist

Problems(1)

Inequality for all positive reals

Source: Balkan MO ShortList 2008 A1

4/5/2020
For all α1,α2,α3∈R+\alpha_1, \alpha_2,\alpha_3 \in \mathbb{R}^+, Prove \begin{align*} \sum \frac{1}{2\nu \alpha_1 +\alpha_2+\alpha_3} > \frac{2\nu}{2\nu +1} \left( \sum \frac{1}{\nu \alpha_1 + \nu \alpha_2 + \alpha_3} \right) \end{align*} for every positive real number ν\nu
Inequalityinequalities