Max and min part 1

Algebra Level 5

\[\large \frac{a}{1+bc}+\frac{b}{1+ac}+\frac{c}{1+ab}\] If \(a,b\) and \(c\) are non-negative reals satisfying \(a^2+b^2+c^2=1\), find the sum of the maximum and minimum value of the expression above.

Submit your answer to 3 decimal places.

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