[ Cubic Polynomials]

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

#
$3 x^{3}+3 x^{2}+3 x+1=0 \Leftrightarrow 2 x^{3}=-(x+1)^{3} \Leftrightarrow \sqrt[3]{2} x=-x-1$.

## Answer

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