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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 $a + b$.

 May 29, 2024
 #1
avatar+820 
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Not too bad of a problem. 

\( \frac{b^2 - a^2}{ b - a } = \frac{ (b -a) (b + a)}{(b -a)} = b + a = 2\)

 

Thanks! :)

 Jun 2, 2024

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