ГДЗ по алгебре 8 класс Мерзляк Задание 738

\[\boxed{\mathbf{738\ (738).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[\frac{x_{1}}{x_{2}} + \frac{x_{2}}{x_{1}} = \frac{5}{2}\]

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

\[= \frac{5}{2}\]

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

\[x_{1} \cdot x_{2} = 8\]

\[x_{1} + x_{2} = a\]

\[\frac{a^{2} - 16}{8} = \frac{5}{2}\]

\[a^{2} - 16 = 20\]

\[a^{2} = 36\]

\[a = 6;\ \ \ \ a = - 6\]

\[Ответ:a = 6\ или\ a = - 6.\]