Решебник по алгебре 7 класс Мерзляк Задание 736

\[\boxed{\text{736\ (736).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[x_{1} - x_{2} = 8;\ \ \ \ \ x_{1}x_{2} = 5\]

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

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

\[= 5 \cdot ( - 8) = - 40\]

\[2)\text{\ x}_{1}² + x_{2}² =\]

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

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

\[= 8^{2} + 2 \cdot 5 = 64 + 10 = 74\]

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

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

\[= 8^{2} + 4 \cdot 5 = 64 + 20 = 84\]

\[4)\ x_{1}³ - x_{2}^{3} =\]

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

\[= 8 \cdot \left( \underset{из\ п.2}{\overset{74}{︸}} + 5 \right) =\]

\[= 8 \cdot 79 = 632\]