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2005 IMO Problems/Problem 3

Revision as of 12:15, 23 August 2020 by Pureswag (talk | contribs) (Created page with "Let <math>x, y, z > 0</math> satisfy <math>xyz\ge 1</math>. Prove that <cmath>\frac{x^5-x^2}{x^5+y^2+z^2} + \frac{y^5-y^2}{x^2+y^5+z^2} + \frac{z^5-z^2}{x^2+y^2+z^5} \ge 0.</c...")
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Let $x, y, z > 0$ satisfy $xyz\ge 1$. Prove that \[\frac{x^5-x^2}{x^5+y^2+z^2} + \frac{y^5-y^2}{x^2+y^5+z^2} + \frac{z^5-z^2}{x^2+y^2+z^5} \ge 0.\]

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