$2+$ $[$ higher degree equations (miscellaneous). ]

Solve the equation $\left[x^{3}\right]+\left[x^{2}\right]+[x]=\{x\}-1$.

#
The number on the left is an integer, and, consequently, the number on the right is also an integer, that is, $\{x\}=0$. Therefore, $x$ is an integer, so the equation can be rewritten as $x^{3}+x^{2}+x=-1$, or $(x+1)\left(x^{2}+1\right)=0$.

## Answer

$x=-1$.