Question 21
Let $a,$ $b,$ and $c$ be positive integers with $a \ge b \ge c$ such that $$
a^2 - b^2 - c^2 + ab = 2011
$$ and $$
\begin{aligned} &a^2 + 3b^2 + 3c^2 \\ &\quad {}- 3ab - 2ac - 2bc = -1997. \end{aligned}
$$
What is $a?$
a^2 - b^2 - c^2 + ab = 2011
$$ and $$
\begin{aligned} &a^2 + 3b^2 + 3c^2 \\ &\quad {}- 3ab - 2ac - 2bc = -1997. \end{aligned}
$$
What is $a?$