Решебник по алгебре 8 класс Мерзляк Задание 737

\[\boxed{\mathbf{737\ (737).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[x_{1}² + x_{2}² = \frac{46}{9}\]

\[x_{1}^{2} + x_{2}^{2} + 2x_{1}x_{2} - 2x_{1}x_{2} =\]

\[= \left( x_{1} + x_{2} \right)^{2} - 2x_{1}x_{2} = \frac{46}{9}\]

\[3x^{2} + ax - 7 = 0\]

\[x_{1}x_{2} = - \frac{7}{3}\]

\[x_{1} + x_{2} = - \frac{a}{3}\]

\[\left( - \frac{a}{3} \right)^{2} + \frac{2 \cdot 7}{3} = \frac{46}{9}\]

\[\frac{a^{2}}{9} + \frac{14}{3} = \frac{46}{9}\]

\[\frac{a^{2}}{9} = \frac{46}{9} - \frac{14}{3}\]

\[\frac{a^{2}}{9} = \frac{4}{9}\]

\[a^{2} = 4\]

\[a = 2;\ \ \ \ a = - 2\]

\[Ответ:\ a = - 2\ \ или\ a = \ 2.\]