\(\begin{array}{l}
P = x - \sqrt x - 2013\,\left( {x \ge 0} \right)\\
= {\left( {\sqrt x } \right)^2} - 2.\frac{1}{2}\sqrt x + \frac{1}{4} - \frac{1}{4} - 2013\\
= {\left( {\sqrt x - \frac{1}{2}} \right)^2} - \frac{{8053}}{4} \ge - \frac{{8053}}{4}\\
GTNN\,P = - \frac{{8053}}{4} \Leftrightarrow \sqrt x = \frac{1}{2} \Leftrightarrow x = \frac{1}{4}\left( {tm} \right)
\end{array}\)