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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