Решите неравенство: x^4-3x^3<=(81x-243)/x.

\[x^{4} - 3{x^{3}}^{\backslash x} \leq \frac{81x - 243}{x}\]

\[\frac{\left( x^{4} - 3x^{3} \right)x - (81x - 243)}{x} \leq 0\]

\[\frac{x^{4}(x - 3) - 81 \cdot (x - 3)}{x} \leq 0\]

\[\frac{(x - 3)(x^{4} - 81)}{x} \leq 0\]

\[\frac{(x - 3)(x^{2} - 9)(x^{2} + 9)}{x} \leq 0\]

\[\frac{(x - 3)^{2}(x + 3)}{x} \leq 0\]

\[Ответ:\lbrack - 3;0) \cup \left\{ 3 \right\}.\]