Question: Use Lagrange multipliers to find the indicated extrema

\[\begin{aligned} & \text{Maximize}\,\,\,\,\,f\left( x,y,z \right)=xyz \\ & \text{s}\text{.t}\text{.}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}^{2}}+{{z}^{2}}=5 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x-2y=0 \\ \end{aligned}\]