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МатематикаРешебник по алгебре 9 класс Мерзляк Задание 738
Задание 738
\[\boxed{\mathbf{738\ (738).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ \left\{ \begin{matrix} a_{5} + a_{12} = 41\ \ \\ a_{10} + a_{14} = 62 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} a_{1} + 4d + a_{1} + 11d = 41 \\ a_{1} + 9d + a_{1} + 13d = 62 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\text{\ \ \ \ }\left\{ \begin{matrix} 2a_{1} + 15d = 41 \\ 2a_{1} + 22d = 62 \\ \end{matrix} \right.\ \ ( - )\]
\[\left\{ \begin{matrix} - 7d = - 21\ \ \ \ \ \\ a_{1} = \frac{41 - 15d}{2} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} d = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ a_{1} = \frac{41 - 45}{2} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} d = 3\ \ \ \ \\ a_{1} = - 2 \\ \end{matrix} \right.\ \]
\[Ответ:\ a_{1} = - 2;\ \ d = 3.\]
\[2)\left\{ \begin{matrix} a_{7} + a_{13} = - 104 \\ a_{2} \cdot a_{6} = - 240 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} a_{1} + 6d + a_{1} + 12d = - 104 \\ \left( a_{1} + d \right)\left( a_{1} + 5d \right) = - 240\ \ \ \\ \end{matrix} \right.\ \]
\[\ \left\{ \begin{matrix} 2a_{1} + 18d = - 104\ \ \ \ \ \ \ |\ :2 \\ \left( a_{1} + d \right)\left( a_{1} + 5d \right) = - 240 \\ \end{matrix} \right.\ \]
\[\ \left\{ \begin{matrix} a_{1} = - 52 - 9d\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ ( - 52 - 9d + d)( - 52 - 9d + 5d) = - 240 \\ \end{matrix} \right.\ \]
\[( - 52 - 8d)( - 52 - 4d) = - 240\ \]
\[- 4 \cdot (13 + 2d) \cdot ( - 4) \cdot\]
\[\cdot (13 + d) = - 240\ \ \ \ |\ :16\]
\[(13 + 2d)(13 + d) = - 15\]
\[169 + 13d + 26d + 2d^{2} +\]
\[+ 15 = 0\]
\[2d^{2} + 39d + 184 = 0\]
\[D = 1521 - 1472 = 49\]
\[d_{1} = \frac{- 39 + 7}{4} = - 8;\ \]
\[\ d_{2} = \frac{- 39 - 7}{4} = - 11,5\]
\[a_{1} = - 52 - 9 \cdot ( - 8) =\]
\[= - 52 + 72 = 20\]
\[a_{1} = - 52 - 9 \cdot ( - 11,5) = 51,5\]
\[Ответ:\ a_{1} = 20;\ d = - 8\ \ \ или\ \]
\[\text{\ \ }a_{1} = 51,5;\ \ d = - 11,5.\]
