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JBMO Shortlist 2022 A3

Source: JBMO Shortlist 2022

June 26, 2023
InequalityJuniorBalkanshortlistalgebra

Problem Statement

Let a,b,a, b, and cc be positive real numbers such that a+b+c=1a + b + c = 1. Prove the following inequality aba3+bcb3+cac3≤ab+bc+ca+23.a \sqrt[3]{\frac{b}{a}} + b \sqrt[3]{\frac{c}{b}} + c \sqrt[3]{\frac{a}{c}} \le ab + bc + ca + \frac{2}{3}.
Proposed by Anastasija Trajanova, Macedonia
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