Road to Math Olympiad Q14

Описание: This question is from RMO 2024.
We are given four real numbers a1, a2, a3, a4 such that
a1^2 + a2^2 + a3^2 + a4^2 = 1
We need to show that there exist indices i and j (with i before j) such that
(a_i - a_j)^2 ≤ 1/5

A neat inequality idea often used in olympiad problems.

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