Решебник по алгебре 9 класс Макарычев Задание 992

\[\boxed{\text{992\ (992).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ x_{1} = ?,\ \ x_{8} = - 128,\]

\[q = - 4,\]

\[x_{8} = x_{1} \cdot q^{7},\]

\[- 128 = x_{1} \cdot ( - 4)^{7}\]

\[x_{1} = \frac{128}{( - 4)^{7}} = \left( \frac{2}{4} \right)^{7} = \frac{1}{128}.\]

\[\textbf{б)}\ x_{1} = 162,\ \ x_{9} = 2,\ \ q = ?\]

\[x_{9} = x_{1} \cdot q^{8},\]

\[2 = 162 \cdot q^{8}\]

\[q^{8} = \frac{2}{162} = \frac{1}{81} = \frac{1}{3^{4}},\]

\[q = \pm \frac{1}{\sqrt{3}} = \pm \frac{\sqrt{3}}{3}.\]