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{align*} \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{align*}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} $.