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МатематикаГДЗ по алгебре 9 класс Мерзляк Задание 461
Задание 461
\[\boxed{\text{461\ (461).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\left\{ \begin{matrix} \frac{1}{x} + \frac{1}{y} = \frac{3}{2} \\ x - y = 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} \frac{1}{x} + \frac{1}{y} = \frac{3}{2} \\ x = 1 + y \\ \end{matrix} \right.\ \]
\[\frac{1^{\backslash 2y}}{1 + y} + \frac{1^{\backslash 2 \cdot (1 + y)}}{y} - \frac{3^{\backslash y \cdot (1 + y)}}{2} = 0\]
\[\frac{2y + 2 + 2y - 3y - 3y^{2}}{2y(1 + y)} = 0\]
\[\left\{ \begin{matrix} - 3y^{2} + y + 2 = 0 \\ y \neq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y \neq - 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[- 3y^{2} + y + 2 = 0\]
\[D = 1 + 24 = 25\]
\[y = \frac{- 1 + 5}{- 6} = - \frac{2}{3}\]
\[y = \frac{- 1 - 5}{- 6} = 1\]
\[\left\{ \begin{matrix} x = 2 \\ y = 1 \\ \end{matrix} \right.\ \ \ \ \ или\ \ \ \left\{ \begin{matrix} x = \frac{1}{3}\text{\ \ \ \ } \\ y = - \frac{2}{3} \\ \end{matrix} \right.\ \]
\[Ответ:(2;1);\ \ \left( \frac{1}{3};\ - \frac{2}{3} \right).\]
\[2)\ \left\{ \begin{matrix} \frac{1}{x} - \frac{1}{y} = \frac{4}{5}\text{\ \ } \\ 3x + y = 8 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} \frac{1}{x} - \frac{1}{y} = \frac{4}{5} \\ y = 8 - 3x \\ \end{matrix} \right.\ \]
\[\frac{1^{\backslash 5 \cdot (8 - 3x)}}{x} - \frac{1^{\backslash 5x}}{8 - 3x} -\]
\[- \frac{4^{\backslash x(8 - 3x)}}{5} = 0\]
\[\frac{40 - 15x - 5x - 32x + 12x^{2}}{5x(8 - 3x)} = 0\]
\[\left\{ \begin{matrix} 12x^{2} - 52x + 40 = 0\ \ |\ :4 \\ x \neq \frac{8}{3}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ x \neq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[3x^{2} - 13x + 10 = 0\]
\[D = 169 - 120 = 49\]
\[x = \frac{13 + 7}{6} = \frac{10}{3}\]
\[x = \frac{13 - 7}{6} = 1\]
\[\left\{ \begin{matrix} x = 1 \\ y = 5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }или\ \ \ \ \left\{ \begin{matrix} x = \frac{10}{3} \\ y = - 2 \\ \end{matrix} \right.\ \]
\[Ответ:(1;5);\ \ \left( 3\frac{1}{3};\ - 2 \right).\]
