Three numbers!

Algebra Level pending

Let \(a\), \(b\) and \(c\) be three distinct real numbers satisfying the conditions: \[\begin{cases} 2a = ab + c \\ 2b = bc + a \\ 2c = ac + b \end{cases} \] Find all possible values of \( a + b + c\).

Clarification: If you have -1, -3 and 2 as solutions, write your answer as -3-12 starting from the smallest number to the largest in a string.

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