Minimizing An Outlandish Expression

Algebra Level 2

\[ \large x \ln x + y \ln y + z \ln z \]

Let \(x,y\) and \(z\) be positive numbers satisfying \(x+y + z= 3e\).

Find the minimum value of the expression above.

\[\] Clarification: \(e \approx 2.71828\) denotes the Euler's number.


Dedicated to Sharky Kesa.
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