Решебник по алгебре 8 класс Мерзляк ФГОС Задание 1135

\[\boxed{\mathbf{1135}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ x² - 4x - 32 = 0\]

\[x_{1} + x_{2} = 4,\ \ x_{1}x_{2} = - 32,\ \ \]

\[x_{1} = 8,\ \ x_{2} = - 4\]

\[Ответ:x = 8;\ x = - 4.\]

\[2)\ x² - 10x + 21 = 0\]

\[x_{1} + x_{2} = 10,\ \ x_{1}x_{2} = 21,\ \ \]

\[x_{1} = 7,\ \ x_{2} = 3\]

\[Ответ:x = 7,x = 3.\]

\[3)\ 6x² - 5x + 1 = 0\]

\[D = 25 - 24 = 1\]

\[x = \frac{5 + 1}{12} = \frac{1}{2}\]

\[x = \frac{5 - 1}{12} = \frac{1}{3}\]

\[Ответ:x = \frac{1}{3};x = \frac{1}{2}.\]

\[4)\ 8x² + 2x - 3 = 0\]

\[D = 4 + 96 = 100\]

\[x = \frac{- 2 + 10}{16} = \frac{1}{2}\]

\[x = \frac{- 2 - 10}{16} = - \frac{3}{4}\]

\[Ответ:x = \frac{1}{2};\ - \frac{3}{4}.\]

\[5)\ x² + 6x - 15 = 0\]

\[D = 36 + 60 = 96\]

\[x = \frac{- 6 \pm 4\sqrt{6}}{2} = - 3 \pm 2\sqrt{6}\]

\[Ответ:\ x = - 3 \pm 2\sqrt{6}.\]

\[6)\ 3x² - x - 5 = 0\]

\[D = 1 + 60 = 61\]

\[x = \frac{1 \pm \sqrt{61}}{6}\]

\[Ответ:\ x = \frac{1 \pm \sqrt{61}}{6}.\]

\[7)\ 4x² + 28x + 49 = 0\]

\[(2x + 7)^{2} = 0\]

\[2x + 7 = 0\]

\[x = - 3,5\]

\[Ответ:\ x = - 3,5.\]

\[8)\ x² - 16x + 71 = 0\]

\[D = 256 - 284 < 0\]

\[Ответ:корней\ нет.\]