Problem

Source: 2018 USAMO Problem 1/USAJMO Problem 2

Tags: 2018 USAMO Problem 1, 2018 USAJMO Problem 2, Inequality, homogenous, Hi



Let \(a,b,c\) be positive real numbers such that \(a+b+c=4\sqrt[3]{abc}\). Prove that \[2(ab+bc+ca)+4\min(a^2,b^2,c^2)\ge a^2+b^2+c^2.\]