Решебник по алгебре 9 класс Мерзляк Задание 772

 

\[\boxed{\mathbf{772\ (772).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[x_{8} = - 14;\ \ x_{30} = - 3\]

\[\left\{ \begin{matrix} x_{1} + 7d = - 14 \\ x_{1} + 29d = - 3 \\ \end{matrix} \right.\ ( - )\text{\ \ \ }\]

\[\ \left\{ \begin{matrix} - 22d = - 11\ \ \ \\ x_{1} = - 14 - 7d \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} d = 0,5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x_{1} = - 14 - 7 \cdot 0,5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} d = 0,5\ \ \ \ \ \ \\ x_{1} = - 17,5 \\ \end{matrix} \right.\ \]

\[S_{40} = \frac{2x_{1} + 39d}{2} \cdot 40 =\]

\[= \left( 2x_{1} + 39d \right) \cdot 20 =\]

\[= \left( 2 \cdot ( - 17,5) + 39 \cdot 0,5 \right) \cdot 20 =\]

\[= \left( - 35 + \frac{39}{2} \right) \cdot 20 =\]

\[= - 700 + 390 = - 310\]

\[Ответ:\ - 310.\]

\[\boxed{\mathbf{772.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[a < b < 2\]

\[a^{2}b + 2b^{2} + 4a < ab^{2} +\]

\[+ 2a^{2} + 4b\]

\[a^{2}b + 2b^{2} + 4a - ab^{2} -\]

\[- 2a^{2} - 4b < 0\]

\[\text{ab}(a - b) + 2 \cdot \left( b^{2} - a^{2} \right) +\]

\[+ 4 \cdot (a - b) < 0\]

\[\text{ab}(a - b) + 2 \cdot (b - a)(b + a) +\]

\[+ 4 \cdot (a - b) < 0\]

\[(a - b)(ab - 2b - 2a + 4) < 0\]

\[(a - b) \cdot\]

\[\cdot \left( b(a - 2) - 2 \cdot (a - 2) \right) < 0\]

\[(a - b)(a - 2)(b - 2) <\]

\[< 0 \Longrightarrow верно.\]