Problem

Source: USAMO 1997/5; also: ineq E2.37 in Book: Inegalitati; Authors:L.Panaitopol,V. Bandila,M.Lascu

Tags: inequalities, AMC, USA(J)MO, USAMO, symmetry, three variable inequality, Hi



Prove that, for all positive real numbers a, b, c, the inequality 1a3+b3+abc+1b3+c3+abc+1c3+a3+abc1abc holds.