Решебник по алгебре 7 класс Мерзляк ФГОС Задание 736

 

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

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

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

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

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

\[2)\text{\ x}_{1}² + x_{2}² =\]

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

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

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

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

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

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

\[4)\ x_{1}³ - x_{2}^{3} =\]

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

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

\[= 8 \cdot 79 = 632\]

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

\[(6x - a)^{2} + (8x - 3)^{2} =\]

\[= (10x - 3)^{2}\]

\[36x^{2} - 12\text{ax} + a^{2} + 64x^{2} - 48x + 9 =\]

\[= 100x^{2} - 60x + 9\]

\[- 12ax + a^{2} - 48x + 9 + 60x - 9 =\]

\[= 0\]

\[12x - 12ax + a^{2} = 0\]

\[12x \cdot (1 - a) + a^{2} = 0\]

\[при\ a = 1:\ \ \]

\[12x \cdot (1 - 1) + 1^{2} = 0\]

\[12x \cdot 0 + 1 = 0\]

\[0x \neq - 1\]

\[нет\ корней.\]

\[Ответ:при\ a = 1.\]