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 $\dfrac{ab}{c}+\dfrac{ac}{b}+\dfrac{bc}{a}$ .