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 $a + b$.
A(a,a2)B(b,b2)b2−a2b−a=2(b+a)(b−a)b−a=2
b+a=2
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+1266 
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