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Algebra Level 4

{a+b+c=2a2+b2+c2=4\large \begin{cases} a+b+c=2 \\ a^2+b^2+c^2=4\end{cases}

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

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