Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 947

\[\left\{ \begin{matrix} 9^{x} \bullet 3^{y} = 9\ \ \ \ \\ \sqrt{y} - \sqrt{x} = 1 \\ \end{matrix} \right.\ \]

\[1)\ 9^{x} \bullet 3^{y} = 9\]

\[3^{2x} \bullet 3^{y} = 3^{2}\]

\[3^{2x + y} = 3^{2}\]

\[2x + y = 2\]

\[y = 2 - 2x.\]

\[2)\ \sqrt{y} - \sqrt{x} = 1\]

\[\sqrt{2 - 2x} - \sqrt{x} = 1\]

\[\sqrt{2 - 2x} = 1 + \sqrt{x}\]

\[2 - 2x = 1 + 2\sqrt{x} + x\]

\[2\sqrt{x} = 1 - 3x\]

\[4x = 1 - 6x + 9x^{2}\]

\[9x^{2} - 10x + 1 = 0\]

\[D = 100 - 36 = 64\]

\[x_{1} = \frac{10 - 8}{2 \bullet 9} = \frac{1}{9};\]

\[x_{2} = \frac{10 + 8}{2 \bullet 9} = 1;\]

\[y_{1} = 2 - \frac{2}{9} = 1\frac{7}{9};\]

\[y_{2} = 2 - 2 = 0.\]

\[Ответ:\ \ (1;\ 0);\ \left( \frac{1}{9};\ 1\frac{7}{9} \right).\]