Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.
Not too bad of a problem.
\( \frac{b^2 - a^2}{ b - a } = \frac{ (b -a) (b + a)}{(b -a)} = b + a = 2\)
Thanks! :)