An inequality may hurt you

Algebra Level 4

(a2a+1)(b2b+1)(c2c+1) (a^2-a+1)(b^2-b+1)(c^2-c+1)

Given that a,ba,b and cc are non-negative numbers and a+b+c=3a+b+c=3, find the sum of the minimum and maximum value of the expression above.


Inspiration.

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