+413 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 $a + b$.
+1946 We know that the slope of AB is 2, which means we can write a formula.
The slope of a line is y2−y1x2−x1. Plugging in the points (a,a2) and (b,b2), we can write the equation
Slope=b2−a2b−a
b2−a2b−a=2
Knowing that b2−a2=(b−a)(b+a), we have
(b−a)(b+a)(b−a)=b+a=2
So our final answer is just 2.
Thanks! :)
