MathDB

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Part of 2022 Serbia JBMO TST

Problems(1)

Inequality with mathematical means

Source: Serbia JBMO TST 2022 P1

6/1/2022
Prove that for all positive real numbers aa, bb 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?
algebrainequalities