3. Given $\frac{1}{a}-|a|=1$, what is the value of $\frac{1}{a}+|a|$? 
(A) $\frac{\sqrt{5}}{2}$
(B) $-\frac{\sqrt{5}}{2}$
(C) $-\sqrt{5}$
(D) $\sqrt{5}$
3. (D).

From the given, we can obtain that $a, \frac{1}{a},|a|$ are all positive, so
$$
\begin{array}{l}
\left(\frac{1}{a}-|a|\right)^{2}=1, \frac{1}{a^{2}}+|a|^{2}=3 \cdot\left(\frac{1}{a}+|a|\right)^{2}=5, \\
\frac{1}{a}+|a|=\sqrt{5} .
\end{array}
$$