What Is The Maximum?

Algebra Level 5

If \(x, y, z \) are real numbers such that \( x + y + z = 3 \), what is the maximum value of

\[ \sqrt{ 2x+13} + \sqrt[3]{3y+5} + \sqrt[4]{8z+12}? \]


This question was posed in SMO 2012. I came across it and it was interesting.
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