Решебник по алгебре 8 класс Мерзляк Задание 695

\[\boxed{\mathbf{695\ (695).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[Уравнение\ имеет\ один\ корень\ \]

\[при\ D < 0.\]

\[1)\ bx² - 6x - 7 = 0\]

\[D = 36 + 28b = 0\]

\[28b = - 36\]

\[b = - \frac{36}{28} = - \frac{9}{7} = - 1\frac{2}{7}\]

\[b = 0:\]

\[\ - 6x - 7 = 0 \Longrightarrow \ \ x = - \frac{7}{6}\]

\[Ответ:при\ b = - 1\frac{2}{7};\ \ \ b = 0.\]

\[2)\ (b + 5)x² - (b + 6)x + 3 = 0\]

\[D = (b + 6)^{2} - 12 \cdot (b + 5) =\]

\[= b^{2} + 12b + 36 - 12b - 60 =\]

\[= b^{2} - 24 = 0\]

\[b^{2} = 24\]

\[b = 2\sqrt{6}\]

\[b = - 2\sqrt{6}\]

\[b + 5 = 0 \Longrightarrow \ \ b = - 5\]

\[Ответ:при\ b = 2\sqrt{6};\ \ \]

\[b = - 2\sqrt{6};\ - 5.\]

\[3)\ (b - 4)x² + (2b - 8)x + 15 =\]

\[= 0\]

\[D = (2b - 8)^{2} - 60 \cdot (b - 4) =\]

\[= 4b^{2} - 92b + 304 = 0\]

\[4b^{2} - 92b + 304 = 0\]

\[b^{2} - 23b + 76 = 0\]

\[D = 529 - 4 \cdot 76 = 225\]

\[b = \frac{23 \pm 15}{2}\]

\[b = 19\]

\[b = 4\ \]

\[2b - 8 \neq 0 \Longrightarrow \ \ b \neq 4\]

\[Ответ:при\ b = 19.\]