Решебник по алгебре 9 класс Мерзляк Задание 802

 

\[\boxed{\mathbf{802\ (802).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[d = 28;\ \ S_{5} = \frac{1}{4} \cdot S_{6 - 11}\]

\[S_{5} = \frac{2a_{1} + 4d}{2} \cdot 5 =\]

\[= \left( a_{1} + 2d \right) \cdot 5 =\]

\[= \left( a_{1} + 2 \cdot 28 \right) \cdot 5 =\]

\[= \left( a_{1} + 56 \right) \cdot 5\]

\[S_{6 - 11} = \frac{2a_{6} + 5d}{2} \cdot 6 =\]

\[= \left( 2 \cdot \left( a_{1} + 5d \right) + 5d \right) \cdot 3 =\]

\[= \left( 2a_{1} + 15d \right) \cdot 3 =\]

\[= \left( 2a_{1} + 15 \cdot 28 \right) \cdot 3 =\]

\[= \left( 2a_{1} + 420 \right) \cdot 3\]

\[5 \cdot \left( a_{1} + 56 \right) =\]

\[= \frac{1}{4} \cdot \left( 2a_{1} + 420 \right) \cdot 3\ \ \ \ | \cdot 4\]

\[20a_{1} + 1120 = 6a_{1} + 1260\]

\[14a_{1} = 140\ \ \]

\[a_{1} = 10\]

\[Ответ:a_{1} = 10.\]

\[\boxed{\mathbf{802.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[y = ax^{2} + bx + c;\ \ ( - 1;0);\ \ \]

\[x_{0} = \frac{1}{4};\ \ y_{0} = - \frac{25}{8}\]

\[- \frac{b}{2a} = \frac{1}{4} \Longrightarrow \ a = - 2b\]

\[0 = a - b + c \Longrightarrow \ - 2b - b + c =\]

\[= 0 \Longrightarrow \ \ - 3b + c = 0 \Longrightarrow \ \ c = 3b\]

\[- \frac{25}{8} = a \cdot \frac{1}{16} + b \cdot \frac{1}{4} + c\ \ \ \ \ | \cdot 8\]

\[- 25 = a \cdot \frac{1}{2} + 2b + 8c\ \ \ \ | \cdot 2\]

\[- 50 = a + 4b + 16c\]

\[- 50 = - 2b + 4b + 16 \cdot 3b\]

\[- 2b + 4b + 48b = - 50\]

\[50b = - 50\]

\[b = - 1\]

\[a = - 2 \cdot ( - 1) = 2;\ \ \]

\[c = 3 \cdot ( - 1) = - 3\]

\[Ответ:a = 2;\ \ b = - 1;\ \ c = - 3.\]