Решебник по алгебре 9 класс Мерзляк Задание 789

 

\[\boxed{\mathbf{789\ (789).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[a_{1} = 105;\ \ d = 7;\ \ \]

\[a_{n} = 105 + 7 \cdot (n - 1) =\]

\[= 105 + 7n - 7 = 7n + 96\]

\[7n + 96 < 1000\]

\[7n < 904\]

\[n < 129,1 \Longrightarrow \ \ \ n = 128\]

\[S_{128} = \frac{2a_{1} + 127d}{2} \cdot 128 =\]

\[= (2 \cdot 105 + 127 \cdot 7) \cdot 64 =\]

\[= (210 + 889) \cdot 64 =\]

\[= 1099 \cdot 64 = 70\ 336.\]

\[Ответ:70\ 336. \]

\[\boxed{\mathbf{790\ (790).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[a_{1} = 8,5;\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ S_{16} = 172\]

\[S_{16} = \frac{2a_{1} + 15d}{2} \cdot 16 =\]

\[= \left( 2a_{1} + 15d \right) \cdot 8\]

\[\left( 2a_{1} + 15d \right) \cdot 8 = 172\]

\[2a_{1} + 15d = 21,5\]

\[- 2 \cdot 8,5 + 21,5 = 15d\]

\[15d = 4,5\]

\[d = 0,3\]

\[Ответ:d = 0,3.\]

\[\boxed{\mathbf{789.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[x^{2} - (2a - 1)x + a^{2} - a -\]

\[- 6 = 0;\ \ x_{1,2} \in \lbrack - 3;2\rbrack\]

\[D = (2a - 1)^{2} -\]

\[- 4 \cdot \left( a^{2} - a - 6 \right) = 4a^{2} - 4a +\]

\[+ 1 - 4a^{2} + 4a + 24 = 25\]

\[x_{1} = \frac{2a - 1 + 5}{2} = \frac{2a + 4}{2} =\]

\[= a + 2\]

\[x_{2} = \frac{2a - 1 - 5}{2} = \frac{2a - 6}{2} =\]

\[= a - 3\]

\[\left\{ \begin{matrix} - 3 \leq a + 2 \leq 2 \\ - 3 \leq a - 3 \leq 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} - 5 \leq a \leq 0 \\ 0 \leq a \leq 5 \\ \end{matrix} \right.\ \Longrightarrow \ \ a = 0\]

\[Ответ:0.\]