ГДЗ по алгебре 8 класс Макарычев Задание 381

\[\boxed{\text{381\ (381).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\sqrt{n^{2} - 75} = m,\ \ где\ m \in N\]

\[\left( \sqrt{n^{2} - 75} \right)^{2} = m^{2}\]

\[n^{2} - 75 = m^{2}\]

\[n^{2} - m^{2} = 75\]

\[(n - m)(n + m) = 75\]

\[\left\{ \begin{matrix} n - m = 1\ \ \\ n + m = 75 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} n = 38\ \ \\ m = 37 \\ \end{matrix} \right.\ \ \]

\[\left\{ \begin{matrix} n - m = 3\ \ \\ n + m = 25 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} n = 14\ \\ m = 11 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} n - m = 5\ \ \\ n + m = 15 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} n = 10 \\ m = 5\ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} n - m = 75 \\ n + m = 1\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} n = 38\ \ \ \ \ \\ m = - 37 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} n - m = 25 \\ n + m = 3\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} n = 14\ \ \ \ \ \\ m = - 11 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} n - m = 15 \\ n + m = 5\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} n = 10\ \ \\ m = - 5 \\ \end{matrix} \right.\ \]

\[Ответ:при\ n = \left\{ 10;14;38 \right\}.\]