Problem

Source: Day2 Problem3

Tags: inequalities, algebra, polynomial, three variable inequality



Find the maximum number $ C$ such that for any nonnegative $ x,y,z$ the inequality $ x^3 + y^3 + z^3 + C(xy^2 + yz^2 + zx^2) \ge (C + 1)(x^2 y + y^2 z + z^2 x)$ holds.