MathDB
JBMO Shortlist 2022 A4

Source: JBMO Shortlist 2022

June 26, 2023
InequalityJuniorBalkanshortlistalgebra

Problem Statement

Suppose that a,b,a, b, and cc are positive real numbers such that a+b+c≥1a+1b+1c.a + b + c \ge \frac{1}{a} + \frac{1}{b} + \frac{1}{c}. Find the largest possible value of the expression a+b−ca3+b3+abc+b+c−ab3+c3+abc+c+a−bc3+a3+abc.\frac{a + b - c}{a^3 + b^3 + abc} + \frac{b + c - a}{b^3 + c^3 + abc} + \frac{c + a - b}{c^3 + a^3 + abc}.
Back to ProblemsView on AoPS