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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 $a + b$.

 Aug 25, 2024
 #1
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We can use the slope the equation and power of a point to solve this question. We have

\([ b^2 - a^2 ] / [ b - a ] = [ (b -a) (b + a) ] / (b -a) = b + a = 2 \)

 

So the answer is 2. 

 

Thanks! :)

 Aug 25, 2024
edited by NotThatSmart  Aug 25, 2024

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