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

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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 $a+b+c=\boxed{5}$ .

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