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MathNet 2012 Question 10

Math Olympiad Vault · MathNet 2012

Question 10

Original English statement:
Let $x$, $y$ and $z$ be positive real numbers. Show that $x^2 + xy^2 + xyz^2 \ge 4xyz - 4$.

Translation of the parallel French statement:
Let $x$, $y$ and $z$ be positive real numbers. Show that $x^2 + xy^2 + xyz^2 \ge 4xyz - 4$.