3. 0 or -1 Explanation: $\tan \alpha=\sqrt{x(x+1)}$, $\sin \beta=\sqrt{x(x+1)+1}, \tan ^{2} \alpha=\sin ^{2} \beta-1=-\cos ^{2} \beta$, $\therefore \tan \alpha=0, \therefore x(x+1)=0$.
3. The solution to the equation $\arctan \sqrt{x(x+1)}+\arcsin \sqrt{x(x+1)+1}=\frac{\pi}{2}$ is