# Extra conditioning

Algebra Level 5

$\begin{cases} a+b+c=a^2 +b^2 \\ ab=c \end{cases}$

Let $P(x) = x^3-2x^2 +px-q$ be a polynomial with roots $a$, $b$ and $c$ satisfying the system of equations above.

Find the sum of all possible values of $p+q$.

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