Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 179

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\[1)\ b_{4} = \frac{1}{27};\ \ b_{6} = \frac{1}{3}:\]

\[b_{5}^{2} = b_{6} \cdot b_{4} = \frac{1}{27} \cdot \frac{1}{3} = \frac{1}{81}\]

\[b_{5} = \frac{1}{9}.\]

\[q = b_{6}\ :b_{5} = \frac{1}{3}\ :\frac{1}{9} = \frac{1}{3} \cdot 9 = 3.\]

\[b_{4} = b_{1} \cdot q^{3}\]

\[b_{1} = b_{4}\ :q^{3}\]

\[b_{1} = \frac{1}{27}\ :3^{3} = \frac{1}{27} \cdot \frac{1}{27} = \frac{1}{729}.\]

\[2)\ b_{4} = 36;\ \ b_{6} = 9:\]

\[b_{5}^{2} = b_{4} \cdot b_{6} = 36 \cdot 9 = 324\]

\[b_{5} = 18.\]

\[q = b_{6}\ :b_{5} = 9\ :18 = \frac{1}{2}.\]

\[b_{4} = b_{1} \cdot q^{3}\]

\[b_{1} = b_{4}\ :q^{3}\]

\[b_{1} = 36\ :\left( \frac{1}{2} \right)^{3} = 36 \cdot 8 = 288.\]