\[\frac{\partial U}{\partial x_{1}} = \frac{1}{2} \sqrt{\frac{x_{2}}{x_{1}}}\\
\frac{\partial U}{\partial x_{1}} = \frac{1}{2} \sqrt{\frac{x_{1}}{x_{2}}}\\
\frac{p_{1}}{p_{2}} = \frac{x_{2}}{x_{1}}\\
p_{1}x_{1}= p_{2}x_{2} = I\\
x_{1} = \frac{I}{2p_{1}}\\
x_{2} = \frac{I}{2p_{2}}\]