Решебник по алгебре 8 класс Мерзляк ФГОС Задание 744

 

\[\boxed{\mathbf{744\ (744).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[x_{1}² + x_{2}² = 9\]

\[\left( x_{1} + x_{2} \right)^{2} - 2x_{1}x_{2} = 9\]

\[x^{2} + (a - 1)x - 2a = 0\]

\[x_{1} + x_{2} = 1 - a\]

\[x_{1}x_{2} = - 2a\]

\[(1 - a)^{2} + 4a = 9\]

\[1 - 2a + a^{2} + 4a - 9 = 0\]

\[a^{2} + 2a - 8 = 0\]

\[a = - 4 \Longrightarrow не\ подходит.\]

\[a = 2\]

\[Ответ:при\ a = 2.\]

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

\[1)\ x² + 6x - 32 = 0\]

\[x_{1} + x_{2} = - 6\]

\[x_{1}x_{2} = - 32\]

\[2)\ x² - 10x + 4 = 0\]

\[x_{1} + x_{2} = 10\]

\[x_{1}x_{2} = 4\]

\[3)\ 2x² - 6x + 3 = 0\]

\[x_{1} + x_{2} = \frac{6}{2} = 3\]

\[x_{1}x_{2} = \frac{3}{2} = 1,5\]

\[4)\ 10x² + 42x + 25 = 0\]

\[x_{1} + x_{2} = - \frac{42}{10} = - 4,2\]

\[x_{1}x_{2} = \frac{25}{10} = 2,5\]