Решите уравнение 81x^3+18x^2+x=0.

Ответ:

\[81x^{3} + 18x^{2} + x = 0\]

\[x\left( 81x^{2} + 18x + 1 \right) = 0\]

\[x(9x + 1)^{2} = 0\]

\[x = 0;\ \ \ \ \ \ \ \ \ 9x + 1 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 9x = - 1\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - \frac{1}{9}\]

\[Ответ:x = - \frac{1}{9};\ \ x = 0.\]