Question 19
Let $a$, $b$, $c$ and $d$ be non-negative real numbers satisfying $a + b + c + d = 2$. Prove that
$$
(a^2 + b^2)(b^2 + c^2)(c^2 + d^2)(d^2 + a^2) \le 1.
$$
$$
(a^2 + b^2)(b^2 + c^2)(c^2 + d^2)(d^2 + a^2) \le 1.
$$
MathNet 2015-part-04 — 191 problems (EN–VI) Question 19
Math Olympiad Vault · MathNet 2015-part-04 — 191 problems (EN–VI)