Problem

Source: 2021 Iran second round mathematical Olympiad P5

Tags: combinatorics, algebra, inequalities, Iran



1400 real numbers are given. Prove that one can choose three of them like $x,y,z$ such that : $$\left|\frac{(x-y)(y-z)(z-x)}{x^4+y^4+z^4+1}\right| < 0.009$$