6

Part of 2014 Czech and Slovak Olympiad III A

Problems(1)

Source: 2014 Czech & Slovak Mathematical Olympiad, Rnd. III, Cat. A

For arbitrary non-negative numbers

a

b

prove inequality

\frac{a}{\sqrt{b^2+1}}+\frac{b}{\sqrt{a^2+1}}\ge\frac{a+b}{\sqrt{ab+1}}

, and find, where equality occurs.
(Day 2, 6th problem authors: Tomáš Jurík, Jaromír Šimša)

inequalitiesBPSQ