Решебник по алгебре 9 класс Макарычев Задание 1073

 

\[\boxed{\text{1073\ (1073).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[Пусть\ x_{1},x_{2},x_{3} - три\ числа,\ \]

\[составляющие\ геометрическую\ \]

\[прогрессию.\]

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

\[x_{2} = x_{1}q,\ \ x_{3} = x_{2}q,\]

\[S_{3} = \frac{x_{1}\left( q^{3} - 1 \right)}{q - 1} = - 3,\]

\[\frac{x_{1}(q - 1)(q^{2} + q + 1)}{q - 1} = - 3\]

\[x_{1}\left( q^{2} + q + 1 \right) = - 3\]

\[q^{2} + q + 1 > 0 \Longrightarrow при\ любом\ q,\ \ \]

\[x_{1} < 0.\]

\[1)\ x_{1} = - 1,\]

\[q^{2} + q + 1 = 3\]

\[q^{2} + q - 2 = 0\]

\[D = 1 + 8 = 9\]

\[q_{1} = - 2 \Longrightarrow b_{1} = - 1,\ \ \]

\[b_{2} = 2,\ \ b_{3} = - 4;\ \]

\[q_{2} = 1 \Longrightarrow b_{1} = - 1,\ \ \]

\[b_{2} = - 1,\ \ b_{3} = - 1.\]

\[2)\ x_{2} = - 2,\]

\[q^{2} + q + 1 = 1,5\]

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

\[D = 4 + 8 = 12\]

\[q_{1,2} = \frac{- 2 \pm 2\sqrt{3}}{4} = \frac{- 1 \pm \sqrt{3}}{2} \Longrightarrow\]

\[\Longrightarrow не\ подходит\ по\ условию.\]

\[3)\ x_{3} = - 3,\]

\[q^{2} + q + 1 = 0\]

\[q^{2} + q = 0\]

\[q(q + 1) = 0\]

\[q = 0 \Longrightarrow не\ подходит\ по\ \]

\[условию.\]

\[q = - 1 \Longrightarrow b_{1} = - 3,\ \ b_{2} = 3,\]

\[b_{3} = - 3.\]

\[4)\ x_{4} = - 4,\]

\[q^{2} + q + 1 = 0,75\]

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

\[D = 16 - 16 = 0\]

\[q = - \frac{1}{2} \Longrightarrow b_{1} = - 4,\ \ b_{2} = 2,\ \ \]

\[b_{3} = - 1.\]

\[5)\ x_{5} = - 5,\]

\[q² + q + 1 = 0,6\]

\[5q^{2} + 5q + 2 = 0\]

\[D = 25 - 40 = - 15 < 0 \Longrightarrow нет\ \]

\[решения.\]

\[Ответ:\ 1)\ - 1;2;\ - 4;\ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ 2)\ - 1;\ - 1;\ - 1;\ \ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ 3) - 3;3;\ - 3;\ \ \ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ 4)\ - 4;2;\ - 1.\]