Cocassi Function

Algebra Level 2

\[ \large \begin{cases} { a(b+c)=32 } \\ { b(c+a) = 65 } \\ {c(a+b) = 77 } \end{cases}\]

Given that \(a , b,\) and \( c\) are positive real numbers that satisfy the system of equations above, find the value of \(abc\).

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