Let-a-b-c-gt-0-and-a-b-c-3-Prove-that-a-2021-b-2021-c-2021-3-1-4042-3-1-ab-bc-ca-3-

Question Number 144421 by loveineq last updated on 25/Jun/21

Let a, b, c > 0 and a + b + c = 3 . Prove that

\frac{a^{2021} + b^{2021} + c^{2021}}{3} ⩾ 1 + \frac{4042}{3} (1 - \frac{a b + b c + c a}{3})