Serbia JBMO TST 2021 problem 1
Source: Serbia JBMO TST 2021
January 3, 2022
algebrainequalities
Problem Statement
Prove that for positive real numbers the following inequality holds:
\begin{align*}
\frac{a}{9bc+1}+\frac{b}{9ca+1}+\frac{c}{9ab+1}\geq \frac{a+b+c}{1+(a+b+c)^2}
\end{align*}
When does equality occur?