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МатематикаРешебник по алгебре и начала математического анализа 10 класс Колягин Задание 265
Задание 265
\[\boxed{\mathbf{265}.}\]
\[1)\ x^{2} - y^{2} = 21\]
\[(x - y)(x + y) = 21\]
\[\left\{ \begin{matrix} x - y = 1\ \ \\ x + y = 21 \\ \end{matrix} \right.\ ( + )\]
\[2x = 22\]
\[x = 11.\]
\[y = x - 1 = 11 - 1 = 10.\]
\[\left\{ \begin{matrix} x - y = - 1\ \ \\ x + y = - 21 \\ \end{matrix} \right.\ ( + )\]
\[2x = - 22\]
\[x = - 11.\]
\[y = x + 1 = - 11 + 1 = - 10.\]
\[\left\{ \begin{matrix} x - y = 21 \\ x + y = 1\ \ \ \\ \end{matrix} \right.\ ( + )\]
\[2x = 22\]
\[x = 11.\]
\[y = 1 - x = 1 - 11 = - 10.\]
\[\left\{ \begin{matrix} x - y = - 21 \\ x + y = - 1\ \ \\ \end{matrix} \right.\ ( + )\]
\[2x = - 22\]
\[x = - 11.\]
\[y = - 1 - x = - 1 + 11 = 10.\]
\[\left\{ \begin{matrix} x - y = 3 \\ x + y = 7 \\ \end{matrix} \right.\ ( + )\]
\[2x = 10\]
\[x = 5.\]
\[y = x - 3 = 5 - 3 = 2.\]
\[\left\{ \begin{matrix} x - y = - 3 \\ x + y = - 7 \\ \end{matrix} \right.\ ( + )\]
\[2x = - 10\]
\[x = - 5.\]
\[y = - 7 - x = - 7 + 5 = - 2.\]
\[\left\{ \begin{matrix} x - y = 7 \\ x + y = 3 \\ \end{matrix} \right.\ ( + )\]
\[2x = 10\]
\[x = 5.\]
\[y = x - 7 = 5 - 7 = - 2.\]
\[\left\{ \begin{matrix} x - y = - 7 \\ x + y = - 3 \\ \end{matrix} \right.\ ( + )\]
\[2x = - 10\]
\[x = - 5.\]
\[y = - 3 - x = - 3 + 5 = 2.\]
\[Ответ:(11;10);( - 11; - 10);\]
\[(11; - 10);( - 11;10);\]
\[(5;2);( - 5; - 2);\]
\[(5; - 2);( - 5;2).\]
\[2)\ xy = 5 - x\]
\[xy + x = 5\]
\[x(y + 1) = 5\]
\[\left\{ \begin{matrix} x = 1\ \ \ \ \ \ \ \\ y + 1 = 5 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 1 \\ y = 4 \\ \end{matrix} \right.\ ;\]
\[\left\{ \begin{matrix} x = - 1\ \ \ \ \ \ \ \ \\ y + 1 = - 5 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = - 1 \\ y = - 6 \\ \end{matrix} \right.\ ;\]
\[\left\{ \begin{matrix} x = 5\ \ \ \ \ \ \ \ \\ y + 1 = 1 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 5 \\ y = 0 \\ \end{matrix} \right.\ ;\]
\[\left\{ \begin{matrix} x = - 5\ \ \ \ \ \ \ \ \\ y + 1 = - 1 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = - 5 \\ y = - 2 \\ \end{matrix} \right.\ .\]
\[Ответ:(1;4);\ \ ( - 1; - 6);\]
\[\text{\ \ }(5;0);\ \ ( - 5; - 2).\]
