Inequality with mathematical means
Source: Serbia JBMO TST 2022 P1
June 1, 2022
algebrainequalities
Problem Statement
Prove that for all positive real numbers , the following inequality holds:
\begin{align*}
\sqrt{\frac{a^2+b^2}{2}}+\frac{2ab}{a+b}\ge \frac{a+b}{2}+ \sqrt{ab}
\end{align*}
When does equality hold?