Решебник по алгебре 9 класс Мерзляк Задание 807

 

\[\boxed{\mathbf{807\ (807).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[\frac{a_{1} + a_{2} + \ldots + a_{n}}{n} = \frac{S_{n}}{n} =\]

\[= \frac{2a_{1} + d(n - 1)}{2n} \cdot n =\]

\[= \frac{2a_{1} + dn - d}{2}\]

\[\frac{2a_{1} + dn - d}{2} = n\ \ \]

\[2a_{1} + dn - d = 2n\]

\[2a_{1} - 2n = d - dn\]

\[2 \cdot \left( a_{1} - n \right) = d(1 - n)\text{\ \ }\]

\[подбираем\ \ a_{1}\ и\ d;\ \ тогда:\]

\[a_{1} = 1;\ \ d = 2.\]

\[Ответ:\ a_{1} = 1;\ \ d = 2.\]

\[\boxed{\mathbf{807.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{1}{3}x² + 3x + 6 < 0\]

\[D = 9 - 8 = 1\]

\[x = \frac{- 3 + 1}{\frac{2}{3}} = - \frac{6}{2} = - 3\]

\[x = \frac{- 3 - 1}{\frac{2}{3}} = - \frac{12}{2} = - 6\]

\[Ответ:\ x = - 5;\ - 4.\]

\[2) - 4x^{2} + 3x + 1 \geq 0\]

\[D = 9 + 16 = 25\]

\[x = \frac{- 3 + 8}{- 8} = - \frac{1}{4}\]

\[x = \frac{- 3 - 5}{- 8} = 1\]

\[Ответ:x = 1.\]