Решебник по алгебре 9 класс Мерзляк Задание 1026

\[\boxed{\mathbf{1026\ (1026).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[Пусть\ числа\ a_{1},\ a_{2},\ a_{3},\]

\[3a_{1}^{2} + 24a_{1} - 6a_{1}^{2} +\]

\[+ 5 \cdot \left( 16 - 8a_{1} + a_{1}^{2} \right) = 80\]

\[3a_{1}^{2} + 24a_{1} - 6a_{1}^{2} + 80 -\]

\[- 40a_{1} + 5a_{1}^{2} = 80\]

\[2a_{1}^{2} - 16a_{1} = 0,\ \ \]

\[2a_{1}\left( a_{1} - 8 \right) = 0,\ \ \]

\[a_{1} = 0\ \ или\ \ \ a_{1} = 8\]

\[a_{1} = 0,\ \ a_{2} = a_{1} + d,\ d = 4 -\]

\[- a_{1} = 4,\ \ a_{2} = 0 + 4 = 4,\ \ \]

\[a_{3} = 4 + 4 = 8\]

\[a_{1} = 8,\ \ d = 4 - 8 = - 4,\]

\[\text{\ \ }a_{2} = 8 - 4 = 4,\ \ \]

\[a_{3} = 4 - 4 = 0\]

\[Ответ:0;4;8.\]