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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 $a + b$.

 Jul 1, 2024
 #1
avatar+129733 
+1

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

 

So

 

a + b  =  2

 

cool cool cool

 Jul 1, 2024

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