AoPS Wiki talk:Problem of the Day/September 18, 2011
Revision as of 08:01, 18 September 2011 by Negativebplusorminus (talk | contribs) (Created page with "=Solution= We see that for positive <math>x</math>, <cmath>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}</cmath> a...")
Solution
We see that for positive 
,
![\[f(x)=\sqrt{(x^3+3x+0)(x^2+3x+2)+1}=\sqrt{((x^2+3x+1)-1)((x^2+3x+1)-1)+1}=\sqrt{(x^2+3x+1)^2}=\boxed{x^2+3x+1}\]](http://latex.artofproblemsolving.com/a/9/c/a9c0c4bb11b96580e21bc64eac193c3b3bc00088.png)
and thus 
.
