Решебник по алгебре 8 класс Мерзляк Задание 733

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

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

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

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

\[D = 64 + 12 = 76\]

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

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

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

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

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

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

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

\[= 36 - 19 = 17\]

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

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

\[Получаем\ уравнение:\ \]

\[x² + 12x + 17 = 0.\]