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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