MathDB

Inequality

Source: Romanian JBMO TST1 2017 P2

May 4, 2017

inequalitiesinequalities proposedalgebra

Problem Statement

a) Find :

A=\{(a,b,c) \in \mathbb{R}^{3} | a+b+c=3 , (6a+b^2+c^2)(6b+c^2+a^2)(6c+a^2+b^2) \neq 0\}

b) Prove that for any

(a,b,c) \in A

next inequality hold :
\begin{align*} \frac{a}{6a+b^2+c^2}+\frac{b}{6b+c^2+a^2}+\frac{c}{6c+a^2+b^2} \le \frac{3}{8} \end{align*}