IMC 2011 — Keystage 3 (IWYMIC) — individual Question 14

For $a=1,2,\ldots,2011$, the roots of $x^2-2x-a^2-a=0$ are $\alpha_a,\beta_a$. Evaluate $\sum_{a=1}^{2011}(1/\alpha_a+1/\beta_a)$.