Решебник по алгебре 8 класс Мерзляк ФГОС Задание 784

 

\[\boxed{\mathbf{784\ (784).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{x^{2} - 9x - 10}{x^{2} - 1} = 0;\ \ \ \ \ \ x \neq 1;\ \ \ \ \]

\[x \neq - 1\]

\[x^{2} - 9x - 10 = 0\]

\[x_{1} + x_{2} = 9,\ \ x_{1}x_{2} = - 10,\ \]

\[\ x_{1} = 10,\ \ \]

\[x_{2} = - 1\ (не\ подходит)\]

\[Ответ:x = 10.\]

\[2)\ \frac{x^{2} + 5x - 14}{x^{2} - 6x + 8} = 0\]

\[x^{2} - 6x + 8 \neq 0\]

\[x_{1} + x_{2} = 6;\ \ \ \ \ \ x_{1} \cdot x_{2} = 8\]

\[x_{1} \neq 4;\ \ \ \ \ x_{2} \neq 2\]

\[x^{2} + 5x - 14 = 0\]

\[x_{1} + x_{2} = - 5;\ \ \ \ \ x_{1} \cdot x_{2} = - 14\]

\[x_{1} = - 7;\ \ \ \ \ \ \]

\[x_{2} = 2\ \ (не\ подходит)\]

\[Ответ:\ x = - 7.\]

\[\boxed{\mathbf{7}\mathbf{8}\mathbf{4}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[\left\{ \begin{matrix} y = x^{2}\text{\ \ \ \ \ } \\ y = x + 2 \\ \end{matrix} \right.\ \]

\[x^{2} = x + 2\]

\[x^{2} - x - 2 = 0\]

\[D = 1 + 8 = 9\]

\[x = \frac{1 \pm 3}{2}\]

\[x = 2,\ \ y = 4\]

\[x = - 1,\ \ y = 1\]

\[\text{C\ }(2;4);\ \ \ \ \text{B\ }( - 1;1)\]

\[y = x^{2}\]

\[y = x + 2\]