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.
by
Guillermo Templado