2. Given $a=\sqrt{3}-1$. Then the value of $a^{2012}+2 a^{2011}-$ $2 a^{2010}$ is $\qquad$.
2. 0 .

From the condition we know
$$
\begin{array}{l}
(a+1)^{2}=3 \Rightarrow a^{2}+2 a-2=0 \text {. } \\
\text { Then } a^{2012}+2 a^{2011}-2 a^{2010} \\
=a^{2010}\left(a^{2}+2 a-2\right)=0 .
\end{array}
$$