Question 63
Prove that among any 9 distinct real numbers, there exist 4 distinct numbers $a$, $b$, $c$, $d$ such that
$$
(ac + bd)^2 \geq \frac{9}{10}(a^2 + b^2)(c^2 + d^2).
$$
$$
(ac + bd)^2 \geq \frac{9}{10}(a^2 + b^2)(c^2 + d^2).
$$
MathNet 2023-part-03 — 191 problems (EN–VI) Question 63
Math Olympiad Vault · MathNet 2023-part-03 — 191 problems (EN–VI)