Unexpectedly Powerful

Algebra Level 4

Consider all triples of real numbers (x,y,z) (x,y,z) such that x,y,z12 x, y, z \geq \frac{1}{2} and x+y+z=3 x+y+z = 3 .

If the minimum and maximum values of xxyyzz x^x y^y z^ z are AA and BB, respectively, what is A+BA+B?

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