Решебник по алгебре 8 класс Мерзляк ФГОС Задание 767

 

\[\boxed{\mathbf{767\ (767).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\left( a^{2} - a - 6 \right)x = a² - 9\]

\[a^{2} - a - 6 = 0\]

\[a_{1} + a_{2} = 1,\ \ a_{1} = - 2\]

\[a_{1} \cdot a_{2} = - 6,\ \ a_{2} = 3\]

\[(a + 2)(a - 3)x = (a - 3)(a + 3)\]

\[x = \frac{(a - 3)(a + 3)}{(a - 3)(a + 2)}\]

\[x = \frac{a + 3}{a + 2}\]

\[если\ a = 3,\ \ \ \]

\[то\ x - любое\ число;\]

\[если\ a = - 2,\ \ \ то\ корней\ нет;\]

\[если\ a \neq 3\ \ и\ \ \ a \neq - 2,\ \ \ \]

\[то\ x = \frac{a + 3}{a + 2}.\]

\[2)\ \left( a^{2} - 8a + 7 \right)x =\]

\[= 2a² - 13a - 7\]

\[(a - 7)(a - 1)x =\]

\[= 2 \cdot (a - 7)(a + 0,5)\]

\[x = \frac{2 \cdot (a - 7)(a + 0,5)}{(a - 7)(a - 1)}\]

\[x = \frac{2 \cdot (a + 0,5)}{a - 1}\]

\[\ если\ a = 7,\ \ \ x - любое\ число.\]

\[если\ a = 1,\ \ \ \ корней\ нет.\]

\[если\ a \neq 1\ \ \ и\ \ a \neq 7,\ \ \ \]

\[то\ x = \frac{2 \cdot (a + 0,5)}{a - 1}.\]

\[\boxed{\mathbf{7}\mathbf{6}\mathbf{7}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ 7x² + 11x - 18 = 0\]

\[x_{1} + x_{2} = - \frac{11}{7},\ \ \]

\[x_{1} = - \frac{18}{7} = - 2\frac{4}{7}\]

\[x_{1} \cdot x_{2} = - \frac{18}{7},\ \ x_{2} = 1\]

\[Ответ:\ \ x = - 2\frac{4}{7};x = 1.\]

\[2)\ 9x² - 5x - 4 = 0\]

\[x_{1} + x_{2} = \frac{5}{9},\ \ x_{1} = - \frac{4}{9}\]

\[x_{1} \cdot x_{2} = - \frac{4}{9},\ \ x_{2} = 1\]

\[Ответ:\ x = - \frac{4}{9};x = 1.\]