Решебник по алгебре 9 класс Мерзляк Задание 750

\[\boxed{\mathbf{750\ (750).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[a_{1} = x^{2} - 4,\ \ a_{2} = 5x + 3,\ \ \]

\[a_{3} = 3x + 2,\ \ тогда\]

\[a_{2} = \frac{a_{1} + a_{3}}{2} \Longrightarrow \ \ 2a_{2} = a_{1} + a_{3}\]

\[2 \cdot (5x + 3) = x^{2} - 4 + 3x + 2\]

\[10x + 6 = x^{2} - 4 + 3x + 2\]

\[x^{2} - 7x - 8 = 0\]

\[x_{1} + x_{2} = 7,\ \ x_{1} = 8\]

\[x_{1}x_{2} = - 8,\ \ x_{2} = - 1\]

\[При\ x_{1} = 8 \Longrightarrow \ a_{1} =\]

\[= 64 - 4 = 60,\ \ \]

\[a_{2} = 40 + 3 = 43,\ \ \]

\[a_{3} = 24 + 2 = 26.\]

\[При\ x_{2} = - 1 \Longrightarrow a_{1} = 1 - 4 =\]

\[= - 3,\ \ a_{2} = - 5 + 3 = - 2,\]

\[\text{\ \ }a_{3} = - 3 + 2 = - 1.\]

\[Ответ:при\ x_{1} = - 1:\ \ \ \]

\[a_{1} = - 3,\ a_{2} = - 2,\ a_{3} = - 1;\ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ при\ x_{2} = 8:\ \ \]

\[\ a_{1} = 60,\ a_{2} = 43,\ a_{3} = 26.\]