How can this possibly be unique...

Algebra Level 3

\[\large \begin{cases} a+b+c=2 \\ a^2+b^2+c^2=4\end{cases} \]

Suppose that \(a,b,\) and \(c\) are nonzero numbers that satisfy the system of equations above. Find \(\dfrac{ab}{c}+\dfrac{ac}{b}+\dfrac{bc}{a}\).