Для каждого значения а решите уравнение: (a^2-a-56)x=a^2-64.

\[\left( a^{2} - a - 56 \right)x = a² - 64\]

\[a^{2} - a - 56 = 0\]

\[a_{1} + a_{2} = 1;\ \ a_{1} \cdot a_{2} = - 56\]

\[\Longrightarrow a_{1} = 8,\ \ a_{2} = - 7.\]

\[a^{2} - a - 56 = (a - 8)(a + 7)\]

\[(a - 8)(a + 7)x =\]

\[= (a - 8)(a + 8)\]

\[a = - 7 \Longrightarrow нет\ решения;\]

\[a = - 8 \Longrightarrow x = 0;\]

\[a \neq - 7;a \neq \pm 8 \Longrightarrow x = \frac{a + 8}{a + 7};\]

\[a = 8:\]

\[\left( 8^{2} - 8 - 56 \right)x = 8^{2} - 64\]

\[0 \cdot x = 0 \Longrightarrow x - любое.\]