Решебник по алгебре 8 класс Мерзляк Задание 731

\[\boxed{\mathbf{731\ (731).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\frac{1}{x_{1}} + \frac{1}{x_{2}} = \frac{x_{1} + x_{2}}{x_{1}x_{2}} = \frac{9}{6} = \frac{3}{2} =\]

\[= 1,5\]

\[2)\ x_{1}² + x_{2}²\ =\]

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

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

\[= 9^{2} - 2 \cdot 6 = 81 - 12 = 69\ \]

\[3)\ \left( x_{1} - x_{2} \right)^{2} =\]

\[= \left( x_{1} + x_{2} \right)^{2} - 4x_{1}x_{2} =\]

\[= 9^{2} - 4 \cdot 6 = 81 - 24 = 57\]

\[4)\ x_{1}³ + x_{2}³ =\]

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

\[= 9 \cdot (69 - 6) = 567\]