11. Satisfy the equation
$$
\begin{array}{l}
\sqrt{x-2009-2 \sqrt{x-2010}}+ \\
\sqrt{x-2009+2 \sqrt{x-2010}}=2 .
\end{array}
$$

All real solutions are
$$
\text { II, 11.2 } 010 \leqslant x \leqslant 2011 \text {. }
$$

Transform the original equation to get
$$
\begin{array}{l}
\sqrt{(\sqrt{x-2010}-1)^{2}}+\sqrt{(\sqrt{x-2010}+1)^{2}}=2 \\
\Rightarrow 0 \leqslant \sqrt{x-2010} \leqslant 1 \\
\Rightarrow 2010 \leqslant x \leqslant 2011 .
\end{array}
$$