No familiar part II

Algebra Level 5

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

Given that x , y x,y and z z are non-negative satisfying x + y + z = 3 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 .


The answer is 7.64.

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