Решебник по алгебре 8 класс Мерзляк ФГОС Задание 707

\[\boxed{\mathbf{707\ (707).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ x² + 6x - 32 = 0\]

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

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

\[2)\ x² - 10x + 4 = 0\]

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

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

\[3)\ 2x² - 6x + 3 = 0\]

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

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

\[4)\ 10x² + 42x + 25 = 0\]

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

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

\[\boxed{\mathbf{707.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[a^{2}x^{2} + 4ax - 5 = 0;\ \ \ \ \ \ \ \ x = \frac{1}{4}\]

\[\frac{1}{16}a² + a - 5 = 0\ \ \ | \cdot 16\]

\[a^{2} + 16a - 80 = 0\]

\[D = 256 + 320 = 576\]

\[a = \frac{- 16 \pm \sqrt{576}}{2} = \frac{- 16 \pm 24}{2}\]

\[a_{1} = - 20\]

\[a_{2} = 4\]

\[Ответ:\ при\ a = - 20;a = 4.\]