No familiar part II

Algebra Level 5

\[\sqrt{x^2-x+1}+\sqrt{y^2-y+1}+\sqrt{z^2-z+1}\]

Given that \(x,y\) and \(z\) are non-negative satisfying \(x+y+z=3\), find the sum of the minimum and the maximum value of the expression above.

Give your answer to two decimal place.


Inspiration.

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