Extra conditioning

Algebra Level 5

{a+b+c=a2+b2ab=c\begin{cases} a+b+c=a^2 +b^2 \\ ab=c \end{cases}

Let P(x)=x32x2+pxqP(x) = x^3-2x^2 +px-q be a polynomial with roots aa, bb and cc satisfying the system of equations above.

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

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