An algebra problem by Rahil Sehgal

Algebra Level 3

If \(a\), \(b\), and \(c\) are positive real numbers such that

\[\frac a{1+a} + \frac b{1+b} + \frac c{1+c} = 1\]

then find the maximum value of \(abc\). Give your answer to 3 decimal places.

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