3. The solution to the equation $x^{2}-|x|-1=0$ is
(A) $\frac{1 \pm \sqrt{5}}{2}$;
(B) $\frac{-1 \pm \sqrt{5}}{2}$;
(C) $\frac{1 \pm \sqrt{5}}{2}$ or $-\frac{1 \pm \sqrt{5}}{2}$;
(D) $\pm \frac{-1+\sqrt{5}}{2}$.
3. (D)

Solution: Let $x_{0}$ be a solution to the equation, then $-x_{0}$ is also a solution to the equation, eliminating (A) and (B); the two values in (D) must be solutions to the equation, otherwise the solutions to the equation would not be (C). Substituting $\frac{1}{2}(1-\sqrt{5})$ into the equation, the left side $\neq 0$, eliminating (C).