\[\boxed{\text{977\ (977).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[y = x^{2} - x + 4\ \ \ и\ \ y = \frac{4}{x},\]
\[x^{3} - x^{2} + 4x - 4 = 0\]
\[x^{2}(x - 1) + 4 \cdot (x - 1) = 0\]
\[\left( x^{2} + 4 \right)(x - 1) = 0\]
\[x^{2} + 4 \neq 0\]
\[\left\{ \begin{matrix} x - 1 = 0 \\ y = \frac{4}{x}\text{\ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 1 \\ y = 4 \\ \end{matrix} \right.\ .\]
\[Ответ:графики\ пересекаются\ \]
\[в\ точке\ (1;4).\]