ГДЗ по алгебре 9 класс Макарычев ФГОС Задание 392

\[\boxed{\text{393.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[x^{2} + \frac{9}{x^{2}} - 10 = 0\ \ \ \ \ \ \ | \cdot x^{2}\]

\[x^{4} - 10x^{2} + 9 = 0\]

\[x^{2} = t:\]

\[t^{2} - 10t + 9 = 0\]

\[D_{1} = 25 - 9 = 16\]

\[t_{1} = 5 + 4 = 9;\ \ \ \ \ \]

\[\ t_{2} = 5 - 4 = 1.\]

\[1)\ x^{2} = 9\]

\[x_{1} = 3;\ \ \ \ x_{2} = - 3;\]

\[y_{1} = \frac{3}{3} = 1;\ \ \ \ y_{2} = \frac{3}{- 3} = - 1.\]

\[2)\ x^{2} = 1\]

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

\[y_{1} = \frac{3}{1} = 3;\ \ \ \ y_{2} = \frac{3}{- 1} = - 3.\]

\[Ответ:(3;1);( - 3; - 1);(1;3);\]

\[( - 1;\ - 3).\]