jmc

By the distance formula, we are trying to minimize $\sqrt{x^2+y^2}=\sqrt{x^2+(1/2)(x^4-6x^2+9)}$. In general, minimization problems like this require calculus, but one optimization method that sometimes works is to try to complete the square. Pulling out a factor of $1/2$ from under the radical, we have $$\begin{array}{rl}\frac{1}{\sqrt{2}}\sqrt{2x^2+x^4-6x^2+9}& =\frac{1}{\sqrt{2}}\sqrt{(x^4-4x^2+4)+5}\\ & =\frac{1}{\sqrt{2}}\sqrt{(x^2-2{)}^2+5}.\end{array}$$This last expression is minimized when the square equals $0$, i.e. when $x=\sqrt{2}$. Then the distance is $\sqrt{5}/\sqrt{2}=\sqrt{10}/2$. Hence the desired answer is $\boxed{12}$.