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MathNet 1989 — Part 01 Question 16

Math Olympiad Vault · MathNet 1989 — Part 01

Question 16

Prove that given seven real numbers, you can choose two, say $a$ and $b$, so that $$
\sqrt{3}|a-b|\lt |1+a b|
$$ give an example of six real numbers that do not meet this property.