Решебник по алгебре 8 класс Мерзляк ФГОС Задание 733

 

\[\boxed{\mathbf{733\ (733).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[x^{2} + 8x - 3 = 0\]

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

\[x_{1} \cdot x_{2} = - 3,\ \ x_{2} = ?\]

\[D = 64 + 12 = 76\]

\[x = \frac{- 8 \pm 2\sqrt{19}}{2} = - 4 \pm \sqrt{19}\]

\[x_{1} = - 4 + \sqrt{19}\]

\[x_{2} = - 4 - \sqrt{19}\]

\[x_{1}^{1}\ = - 4 + \sqrt{19} - 2 = - 6 + \sqrt{19}\]

\[x_{2}^{1} = - 4 - \sqrt{19} - 2 = - 6 - \sqrt{19}\]

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

\[= \left( - 6 + \sqrt{19} \right)\left( - 6 - \sqrt{19} \right) =\]

\[= 36 - 19 = 17\]

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

\[= - 6 + \sqrt{19} - 6 - \sqrt{19} = - 12\]

\[Получаем\ уравнение:\ \]

\[x² + 12x + 17 = 0.\]

\[\boxed{\mathbf{73}\mathbf{3}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ bx² + x + b = 0\]

\[D = 1 - 4b^{2} = 0,\ \ b = 0\]

\[1 - 4b^{2} = 0\]

\[4b^{2} = 1\]

\[b^{2} = \frac{1}{4}\]

\[b = \frac{1}{2},\ \ b = - \frac{1}{2}\]

\[Ответ:при\ b = 0;\ b = \pm 0,5.\]

\[2)\ (b + 3)x² + (b + 1)x - 2 = 0\]

\[D = (b + 1)^{2} + 8 \cdot (b + 3) =\]

\[= b^{2} + 2b + 1 + 8b + 24 =\]

\[= b^{2} + 10b + 25 =\]

\[= (b + 5)^{2} = 0\]

\[(b + 5)^{2} = 0\]

\[b + 5 = 0\]

\[b = - 5\]

\[b + 3 = 0\]

\[b = - 3\]

\[Ответ:\ при\ b = - 5;\ b = - 3.\]