Решебник по алгебре 8 класс Мерзляк ФГОС Задание 768

 

\[\ \boxed{\mathbf{768\ (768).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[\left( a^{2} + 7a - 8 \right)x = a^{2} + 16a + 64\]

\[x = \frac{(a + 8)^{2}}{(a + 8)(a - 1)}\]

\[x = \frac{a + 8}{a - 1},\ \ \]

\[если\ a = - 8,\ \]

\[то\ \ x - любое\ число.\]

\[если\ a = 1,\ то\ \ то\ корней\ нет.\]

\[если\ a \neq - 8\ \ и\ \ a \neq 1,\ \text{\ \ }\]

\[то\ x = \frac{a + 8}{a - 1}.\]

\[\boxed{\mathbf{7}\mathbf{6}\mathbf{8}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

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

\[= 1,5\]

\[2)\ x_{1}² + x_{2}²\ =\]

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

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

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

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

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

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

\[4)\ x_{1}³ + x_{2}³ =\]

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

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