Решебник по алгебре 8 класс Мерзляк ФГОС Задание 672

 

\[\boxed{\mathbf{672\ (672).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

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

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

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

\[D = 256 + 320 = 576\]

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

\[a_{1} = - 20\]

\[a_{2} = 4\]

\[Ответ:\ при\ a = - 20;a = 4.\]

\[\boxed{\mathbf{6}\mathbf{7}\mathbf{2}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ x² - 4x + 3 = 0\]

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

\[(x - 2)^{2} - 1 = 0\]

\[(x - 2 - 1)(x - 2 + 1) = 0\]

\[(x - 3)(x - 1) = 0\]

\[x = 3,\ \ x = 1.\]

\[Ответ:x = 1;x = 3.\]

\[2)\ x² + 6x - 7 = 0\]

\[x^{2} + 6x + 9 - 16 = 0\]

\[(x + 3)^{2} - 16 = 0\]

\[(x + 3 - 4)(x + 3 + 4) = 0\]

\[(x - 1)(x + 7) = 0\]

\[x = 1,\ \ x = - 7\]

\[Ответ:\ x = - 7;x = 1.\]

\[3)\ x² + 8x + 20 = 0\]

\[x^{2} + 8x + 16 + 4 = 0\]

\[(x + 4)^{2} = - 4\]

\[Ответ:нет\ корней.\]