Решебник по алгебре 8 класс Макарычев ФГОС Задание 669

 

\[\boxed{\text{669\ (669).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[Пусть\ x_{1},\ x_{2} -\]

\[последовательные\ \]

\[натуральные\ числа.\]

\[x_{2}^{3} - x_{1}^{3} = 919,\ \ x_{2} = x_{1} + 1\]

\[Составим\ уравнение:\]

\[\left( x_{1} + 1 \right)^{3} - x_{1}^{3} = 919\]

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

\[= 919\]

\[3x_{1}^{2} + 3x_{1} - 918 = 0\ \ \ \ \ \ \ \ |\ :3\]

\[x_{1}^{2} + x_{1} - 306 = 0\]

\[D = 1 + 1224 = 1225 = 35^{2}\]

\[x_{1,2} = \frac{- 1 \pm 35}{2} =\]

\[= 17;\ - 18 < 0\ \ \ \ \varnothing\]

\[x_{1} = 17 \Longrightarrow x_{2} = 18\]

\[Ответ:17\ и\ 18.\ \]

\[\boxed{\text{669.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

\[x^{2} - 10x + q = 0;\ \ \text{\ \ }x_{1} - x_{2} = 6\]

\[по\ теореме\ Виета:\]

\[x_{1} + x_{2} = 10;\ \ \ x_{1}x_{2} = q,\ тогда:\]

\[\left\{ \begin{matrix} x_{1} + x_{2} = 10 \\ x_{1} - x_{2} = 6 \\ \end{matrix} + \right.\ \]

\[x_{1} + x_{2} + x_{1} - x_{2} = 10 + 6\]

\[2x_{1} = 16\]

\[x_{1} = 8\]

\[x_{1} + x_{2} = 10\]

\[x_{2} = 10 - 8 = 2\]

\[q = x_{1}x_{2} = 8 \cdot 2 = 16\]

\[Ответ:q = 16.\ \ \]