An algebra problem by Anish Roy

Algebra Level 3

True or False?

If \(a\), \(b\), and \(c\) are positive real numbers such that \( \dfrac a{a+1} + \dfrac b{b+1} + \dfrac c{c+1} = 1\), then the maximum value of \(abc \) is \( \dfrac18\).

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