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- Feb 14, 2012

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Real numbers $x,\,y$ and $z$ satisfy $x+y+z=4$ and $\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=\dfrac{1}{3}$. Find the largest and smallest possible value of the expression $x^3+y^3+z^3+xyz$.

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