An algebra problem by Dipa Parameswara

Algebra Level 4

Let \(x,y\) and \(z\) be positive numbers satisfying \( \dfrac1x+\dfrac1y + \dfrac1z = 6\). What is the maximum value of \( \dfrac1{x^3 y^2 z} \)?

Give your answer to 2 decimal places.

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