Решебник по алгебре 9 класс Мерзляк Задание 843

 

\[\boxed{\mathbf{843\ (843).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ b_{4} = 9;\ \ b_{6} = 25\ \ \]

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

\[b_{5} = \sqrt{b_{4}b_{6}} = \sqrt{9 \cdot 25} =\]

\[= 3 \cdot 5 = 15\]

\[или\ \ \ \]

\[b_{5} = - \sqrt{9 \cdot 25} = - 15.\]

\[Ответ:\ b_{5} = \pm 15.\]

\[2)\ b_{19} = - 3;\ \ b_{21} = - 12\ \]

\[b_{20} = \pm \sqrt{b_{19}b_{21}} =\]

\[= \pm \sqrt{- 3 \cdot ( - 12)} = \pm \sqrt{36} = \pm 6\]

\[Ответ:\ b_{20} = \pm 6.\]

\[3)\ b_{16} = 2;\ \ b_{18} = 10\]

\[b_{17} = \pm \sqrt{b_{16} \cdot b_{18}} = \pm \sqrt{2 \cdot 10} =\]

\[= \pm \sqrt{20} = \pm 2\sqrt{5}.\]

\[Ответ:\ b_{17} = \pm 2\sqrt{5}.\]

\[\boxed{\mathbf{843.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[8;11;14;\ldots\]

\[d = 11 - 8 = 3\]

\[a_{n} = a_{1} + d(n - 1) = 8 +\]

\[+ 3 \cdot (n - 1) = 8 + 3n -\]

\[- 3 = 3n + 5\]

\[100 < 3n + 5 < 200\]

\[95 < 3n < 195\]

\[\frac{95}{3} < n < 65\]

\[31\frac{2}{3} < n < 65\]

\[Ответ:с\ 32\ по\ 64.\]