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Cyclic inequality with fractions and roots

Source: Baltic Way 2020, Problem 2

November 14, 2020
inequalitiesinequalities proposedcyclic inequalityalgebra

Problem Statement

Let a,b,ca, b, c be positive real numbers such that abc=1abc = 1. Prove that 1ac2+1+1ba2+1+1cb2+1>2.\frac{1}{a\sqrt{c^2 + 1}} + \frac{1}{b\sqrt{a^2 + 1}} + \frac{1}{c\sqrt{b^2+1}} > 2.
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