CZ-SK-MO 2004 Problem 1

Find all triples $(x,y,z)$ of real numbers such that $x^2+y^2+z^2\le 6+\min (x^2-\frac{8}{x^4},y^2-\frac{8}{y^4},z^2-\frac{8}{z^4}).$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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