Exponential maximum

Algebra Level 4

\[ \large { 3 }^{ | x-y | }+{ 3 }^{ | y-z | }+{ 3 }^{ | z-x | } - \sqrt{6x^2+6y^2+6z^2} \]

Let \(x, y\) and \(z\) be real numbers satisfying \(x + y + z = 0 \), find the minimum value of the expression above.


This problem is taken from the 2012 Vietnamese University Entrance Exam.
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