Cocassi Function

Algebra Level 2

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

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

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