Question 6
Given any 7 real numbers, prove that there are two of them, say $x$ and $y$, such that
$$
0 \leq \frac{x-y}{1+xy} \leq \frac{1}{\sqrt{3}}
$$
$$
0 \leq \frac{x-y}{1+xy} \leq \frac{1}{\sqrt{3}}
$$
MathNet 1984 — Part 01 Question 6
Math Olympiad Vault · MathNet 1984 — Part 01