MathDB

\sqrt[3]{x - y + z^3} + \sqrt[3]{y - z + x^3} + \sqrt[3]{z - x + y^3} <= 1

Source: 2006 VMEO III Seniors 11.3 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2463155_vmeo_iii

September 17, 2021

algebrainequalities

Problem Statement

Let

x, y, z

be non-negative real numbers whose sum is

1

. Prove that:

\sqrt[3]{x - y + z^3} + \sqrt[3]{y - z + x^3} + \sqrt[3]{z - x + y^3} \le 1