Let-a-b-c-0-and-a-b-c-4-Prove-that-a-2-ab-b-2-a-b-4-2-b-2-bc-c-2-b-c-4-2-c-2-ca-a-2-c-a-4-2-1-2-

Question Number 141454 by loveineq last updated on 19/May/21

Let a, b, c ⩾ 0 and a + b + c = 4 . Prove that

\frac{a^{2} + a b + b^{2}}{{(a + b + 4)}^{2}} + \frac{b^{2} + b c + c^{2}}{{(b + c + 4)}^{2}} + \frac{c^{2} + c a + a^{2}}{{(c + a + 4)}^{2}} ⩽ \frac{1}{2}