Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 950

\[1)\ \left\{ \begin{matrix} \sqrt{x} + \sqrt{y} = 16 \\ \sqrt{x} - \sqrt{y} = 2\ \ \ \\ \end{matrix} \right.\ \]

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

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

\[y = \left( \sqrt{x} - 2 \right)^{2}.\]

\[\sqrt{x} + \sqrt{y} = 16\]

\[\sqrt{x} + \sqrt{x} - 2 = 16\]

\[2\sqrt{x} = 18\]

\[\sqrt{x} = 9\]

\[x = 81;\]

\[y = 7^{2} = 49.\]

\[Ответ:\ \ (81;\ 49).\]

\[2)\ \left\{ \begin{matrix} \sqrt{x} - \sqrt{y} = 1\ \ \\ \sqrt{x} + \sqrt{y} = 19 \\ \end{matrix} \right.\ \]

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

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

\[y = \left( \sqrt{x} - 1 \right)^{2}.\]

\[\sqrt{x} + \sqrt{y} = 19\]

\[\sqrt{x} + \sqrt{x} - 1 = 19\]

\[2\sqrt{x} = 20\]

\[\sqrt{x} = 10\]

\[x = 100;\]

\[y = 9^{2} = 81.\]

\[Ответ:\ \ (100;\ 81).\]

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