SEAMO 2019 — Paper D — Grade 7–8 Question 24

Numbers $\alpha,\beta$ satisfy $\frac{\alpha^2-\alpha\beta+\beta^2}{\alpha^2+\alpha\beta+\beta^2}=31/43$ and $1/\alpha+1/\beta=7/2$. They are roots of $px^2+qx+r=0$, with integer coefficients of gcd one and p positive. Find p+q+r.