## Problem of the Day #386: Minimization under Constraints
*April 8, 2012*

*Posted by Saketh in : potd , trackback*

Determine the least possible value of the expression

$$ \frac{(x+y^3)\cdot(y+z^3)\cdot(z+x^3)}{xyz} $$

if $x$, $y$, and $z$ are all greater than or equal to some positive real value $n$. Express your answer in terms of $n$.

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