3. Solve the equation: $\left[x^{3}\right]+\left[x^{2}\right]+[x]=\{x\}-1$.
(1972, Kyiv Mathematical Olympiad)
(Note that $\left[x^{3}\right] 、\left[x^{2}\right] 、[x] 、 1$ are all integers, thus $\{x\}=0$, and hence $x$ is an integer; solving yields $x=-1$.)