Решебник по алгебре 9 класс Мерзляк Задание 860

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\[\left\{ \begin{matrix} b_{1} + b_{2} + b_{3} = 168 \\ b_{4} + b_{5} + b_{6} = 21\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} b_{1} + b_{1}q + b_{1}q^{2} = 168\ \ \\ b_{1}q^{3} + b_{1}q^{4} + b_{1}q^{5} = 21 \\ \end{matrix} \right.\ \text{\ \ \ }\]

\[\left\{ \begin{matrix} b_{1}\left( 1 + q + q^{2} \right) = 168 \\ b_{1}q^{3}\left( 1 + q + q^{2} \right) = 21 \\ \end{matrix}|\ : \right.\ \]

\[\frac{b_{1}\left( 1 + q + q^{2} \right)}{b_{1}q^{3}\left( 1 + q + q^{2} \right)} = \frac{168}{21}\text{\ \ }\]

\[\frac{1}{q^{3}} = 8\ \ \]

\[8q^{3} = 1\ \ \]

\[q³ = \frac{1}{8} \Longrightarrow \ \ q = \frac{1}{2}\]

\[b_{1}\left( 1 + \frac{1}{2} + \frac{1}{4} \right) = 168\ \ \]

\[b_{1} \cdot \frac{7}{4} = 168\ \ \]

\[b_{1} = \frac{168 \cdot 4}{7} = 96\]

\[b_{2} = 96 \cdot \frac{1}{2} = 48;\ \ \ \]

\[b_{3} = 48 \cdot \frac{1}{2} = 24;\ \ \]

\[b_{4} = 24 \cdot \frac{1}{2} = 12;\]

\[b_{5} = 12 \cdot \frac{1}{2} = 6;\ \ \]

\[b_{6} = 6 \cdot \frac{1}{2} = 3.\]

\[Ответ:96,\ 48,\ 24,\ 12,\ 6,\ 3.\]