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Inequality where a+b+c=3

Source: Irish Mathematical Olympiad 2023 Problem 8

May 14, 2023
algebrainequalitiesinequalities proposed

Problem Statement

Suppose that a,b,ca, b, c are positive real numbers and a+b+c=3a + b + c = 3. Prove that
a+bc+2+b+ca+2+c+ab+2≥2\frac{a+b}{c+2} + \frac{b+c}{a+2} + \frac{c+a}{b+2} \geq 2
and determine when equality holds.
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