Problem 8

Algebra Level 5

\[\frac{a}{b^3+c^3+1}+\frac{b}{c^3+a^3+1}+\frac{c}{a^3+b^3+1}\]

Given that \(a,b,c\) are non-negative and \(a+b+c=1\). Find the sum of the minimum and maximum value.

Give your answer to two decimal place.


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