\[x^{2} + n^{2}(x - 1) - x = 0\]
\[Пусть\ a\ и\ ( - a) - корни\ \]
\[уравнения.\]
\[Запишем\ систему:\]
\[\left\{ \begin{matrix} a^{2} + n^{2}(a - 1) - a = 0\ \ \ \\ a^{2} + n^{2}( - a - 1) + a = 0 \\ \end{matrix} \right.\ \]
\[a^{2} + n^{2}(a - 1) - a =\]
\[= a^{2} + n^{2}( - a - 1) + a\]
\[an^{2} - n^{2} - a + an^{2} + n^{2} - a =\]
\[= 0\]
\[2an^{2} - 2a = 0\]
\[2an^{2} = 2a\]
\[n^{2} = 1\]
\[n = \pm 1\]
\[Ответ:при\ n = \pm 1.\]