[ [ equations of higher degrees (other)]

Solve the equation $x^{3}+x^{2}+x+1 / 3=0$.

#
Use the formula for the cube of a sum.

## Solution

Transform the equation to the form $(x+1)^{3}=-2 x^{3}$, from which $x+1=-2^{1 / 3} x$.

## Answer

$x=-\frac{1}{1+\sqrt[3]{2}}$