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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 $a + b$.

 Apr 30, 2024
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Using the slope formula gives b2a2ba=2.

 

Note that b2a2=(ba)(a+b) by difference of squares formula. Then, simplifying, we have

 

(ba)(a+b)ba=2a+b=2

 Apr 30, 2024

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