\[\boxed{\text{284}\text{\ (284)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ y^{7} - y^{6} + 8y = 8\]
\[y^{7} - y^{6} + 8y - 8 = 0\]
\[y^{6} \cdot (y - 1) + 8 \cdot (y - 1) = 0\]
\[\left( y^{6} + 8 \right)(y - 1) = 0\]
\[y - 1 = 0\ \ \ \ \ или\ \ \ \ y^{6} + 8 = 0\]
\[y_{1} = 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ y^{6} = - 8 \Longrightarrow\]
\[\Longrightarrow корней\ нет.\]
\[Ответ:y = 1.\]
\[\textbf{б)}\ u^{7} - u^{6} = 64u - 64\]
\[u^{7} - u^{6} - 64u + 64 = 0\]
\[u^{6} \cdot (u - 1) - 64 \cdot (u - 1) = 0\]
\[(u - 1)\left( u^{6} - 64 \right) = 0\]
\[(u - 1)\left( \left( u^{3} \right)^{2} - 8^{2} \right) = 0\]
\[(u - 1)\left( u^{3} - 8 \right)\left( u^{3} + 8 \right) = 0\]
\[u - 1 = 0\ \ \ \ \ или\ \ \ u^{3} = 8\ \ \ или\ \ \]
\[\ u^{3} = - 8\]
\[u_{1} = 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ u_{2} = 2\ \ \ \ \ \ \ \ \ \ \ \ \]
\[\ u_{3} = - 2.\]
\[Ответ:u = 1;\ \ u = \pm 2.\]