$ \begin{aligned}解：&\frac{1}{2}\times(\sqrt{3}-1)^2+\frac{1}{\sqrt{2}}+\sqrt{3} \\ =&\frac{1}{2}\times(3 - 2\sqrt{3}+1)+\frac{\sqrt{2}}{2}+\sqrt{3} \\ =&\frac{1}{2}\times(4 - 2\sqrt{3})+\frac{\sqrt{2}}{2}+\sqrt{3} \\ =&2-\sqrt{3}+\frac{\sqrt{2}}{2}+\sqrt{3} \\ =&2+\frac{\sqrt{2}}{2} \\ \end{aligned}$
