Minimizing An Outlandish Expression

Algebra Level 2

xlnx+ylny+zlnz \large x \ln x + y \ln y + z \ln z

Let x,yx,y and zz be positive numbers satisfying x+y+z=3ex+y + z= 3e.

Find the minimum value of the expression above.

Clarification: e2.71828e \approx 2.71828 denotes the Euler's number.


Dedicated to Sharky Kesa.
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