ГДЗ по алгебре 9 класс Макарычев Задание 59

\[\boxed{\text{59\ (59).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[\textbf{а)}\ x^{2} + x - 6 = 0\]

\[D = 1 + 6 \cdot 4 = 25 = 5^{2}\]

\[x_{1} = \frac{- 1 + 5}{2} = 2;\ \ \ x_{2} =\]

\[= \frac{- 1 - 5}{2} = - 3.\]

\[Ответ:x = 2;\ \ x = - 3.\]

\[\textbf{б)}\ 9x^{2} - 9x + 2 = 0\]

\[D = 9^{2} - 4 \cdot 9 \cdot 2 = 81 - 72 = 9\]

\[x_{1} = \frac{9 + 3}{18} = \frac{12}{18} = \frac{2}{3};\ \ x_{2} =\]

\[= \frac{9 - 3}{18} = \frac{6}{18} = \frac{1}{3}.\]

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

\[\textbf{в)}\ 0,2x^{2} + 3x - 20 = 0\ | \cdot 5\]

\[x^{2} + 15x - 100 = 0\]

\[D = 15^{2} + 400 = 225 + 400 =\]

\[= 625\]

\[x_{1} = \frac{- 15 - 25}{2} = - \frac{40}{2} = - 20;\ \ \ \]

\[x_{2} = \frac{- 15 + 25}{2} = - 5.\]

\[Ответ:x = - 20;\ \ x = 5.\]

\[\textbf{г)} - 2x^{2} - x - 0,125 = 0\ | \cdot ( - 8)\]

\[16x^{2} + 8x + 1 = 0\]

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

\[4x + 1 = 0\]

\[4x = - 1\]

\[x = - \frac{1}{4} = - 0,25\]

\[Ответ:x = - 0,25.\]

\[\textbf{д)}\ 0,1x^{2} + 0,4 = 0\]

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

\[x^{2} = - 4 \Longrightarrow корней\ нет.\]

\[Ответ:решений\ нет.\]

\[\textbf{е)} - 0,3x^{2} + 1,5x = 0\ |\ :( - 0,3)\]

\[x^{2} - 5x = 0\]

\[x(x - 5) = 0\]

\[x_{1} = 0\ \ и\ \ \ x_{2} = 5.\]

\[Ответ:x = 0;x = 5.\]