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 $a + b$.
Find a + b.
\({\color{blue}m_{AB}=2}=\frac{y_b-y_a}{x_b-x_a}=\frac{b^2-a^2}{b-a}=\frac{(b+a)(b-a)}{b-a}\color{blue}=b+a\\ \color{blue}a+b=2\)
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