Art of Problem Solving

AoPS Online

AoPS Wiki talk:Problem of the Day/September 18, 2011

Revision as of 08:01, 18 September 2011 by Negativebplusorminus (talk | contribs)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Solution

We see that for positive $x$ , $\begin{align*}f(x)&=\sqrt{(x^3+3x+0)(x^2+3x+2)+1}\\&=\sqrt{((x^2+3x+1)-1)((x^2+3x+1)-1)+1}\\&=\sqrt{(x^2+3x+1)^2}=\boxed{x^2+3x+1}\end{align*}$ and thus $a+b+c=\boxed{5}$ .

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki_talk:Problem_of_the_Day/September_18,_2011&oldid=42338"

© 2025 AoPS Incorporated