Решебник по алгебре 8 класс Макарычев ФГОС Задание 685

\[\boxed{\text{685\ (685).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[x_{1}^{2} + x_{2}^{2} - 810 = 144\]

\[x_{1}^{2} + x_{2}^{2} = 954\]

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

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

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

\[= ( - p)^{2} - 2 \cdot 405 = 954\]

\[p^{2} - 810 = 954\]

\[p^{2} = 1764\]

\[p = \pm 42\]

\[Ответ:p = \pm 42\text{.\ \ }\]

\[\boxed{\text{685.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

\[\textbf{а)}\ \frac{(2x + 1)(2x - 3)}{4} =\]

\[= x^{2} - 1\ \ \ | \cdot 4\]

\[4x^{2} + 2x - 6x - 3 = 4x^{2} - 4\]

\[- 4x = - 4 + 3\]

\[- 4x = - 1\]

\[x = \frac{1}{4} = 0,25.\]

\[Ответ:x = 0,25.\]

\[\textbf{б)}\ x^{2} - \frac{(2x - 1)x}{2} = 2\ \ \ \ | \cdot 2\]

\[2x^{2} - 2x^{2} + x = 4\]

\[x = 4.\]

\[Ответ:x = 4.\]