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Cyclic inequality with product of fractions

Source: 2023 Junior Macedonian Mathematical Olympiad P3

June 10, 2023
inequalitiesalgebra

Problem Statement

Let aa, bb and cc be positive real numbers such that a+b+c=1a+b+c=1. Prove the inequality (1+ab+2)(1+bc+2)(1+ca+2)≥216. \left ( \frac{1+a}{b}+2 \right ) \left ( \frac{1+b}{c}+2 \right ) \left ( \frac{1+c}{a}+2 \right )\geq 216. When does equality hold?
Proposed by Anastasija Trajanova
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