\[\boxed{\text{477\ (477).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[Пусть\ раствор\ содержал\ \text{x\ }\]
\[грамм\ воды.\ \]
\[(x + 150)\ г - воды\ в\ новом\ \]
\[растворе.\]
\[\frac{50}{x} - была\ концентрация\ соли;\]
\[\frac{50}{x + 150} - концентрация\ соли\ \]
\[в\ новом\ растворе.\]
\[Известно,\ что\ концентрация\]
\[\ уменьшилась\ на\ 7,5\% = 0,075.\]
\[Составим\ уравнение:\]
\[\ \frac{50}{x + 150} = \frac{50}{x} - 0,075\]
\[0,075x^{2} + 11,25x - 7500 = 0\]
\[D = {11,25}^{2} + 4 \cdot 0,075 \cdot 7500 =\]
\[= 2376,5625\]
\[x_{1,2} = \frac{- 11,25 \pm 48,75}{0,15}.\]
\[Так\ как\ x > 0 \Longrightarrow x = 250.\]
\[Концентрация:\ \ \]
\[\frac{50}{250} = 0,2.\]
\[Ответ:250\ грамм;\ \ 20\%.\]
\[\boxed{\text{477.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\textbf{а)}\ \left\{ \begin{matrix} x^{2} + xy = 6 \\ y^{2} + xy = 3 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x^{2} + xy = 6\ \ \ \ \\ 2y^{2} + 2xy = 6 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x^{2} - xy - 2y^{2} = 0 \\ x^{2} - y^{2} = 3\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} (x - 2y)(x + y) = 0 \\ x² - y^{2} = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[1)\ \left\{ \begin{matrix} x = 2y\ \ \ \ \ \ \ \ \ \ \\ 4y^{2} - y^{2} = 3 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x = 2y \\ y^{2} = 1\ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} y_{1} = 1 \\ x_{1} = 2 \\ \end{matrix} \right.\ \text{\ \ \ }или\ \]
\[\left\{ \begin{matrix} y_{2} = - 1 \\ x_{2} = - 2. \\ \end{matrix} \right.\ \]
\[2)\ \left\{ \begin{matrix} x = - y\ \ \ \ \ \ \ \\ y^{2} - y^{2} = 3 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = - y \\ 0 = 3\ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow корней\ нет;\]
\[\textbf{б)}\ \left\{ \begin{matrix} x^{2} - xy = 7 \\ y^{2} - xy = 9 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x - y = \frac{7}{x}\text{\ \ \ \ \ \ } \\ x - y = - \frac{9}{y} \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x - y = \frac{7}{x} \\ \frac{7}{x} = - \frac{9}{y}\text{\ \ \ \ } \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = - \frac{9}{7}x \\ x^{2} = \frac{49}{16}\text{\ \ \ } \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x = \pm 1,75 \\ y = - \frac{9}{7}\text{x\ \ } \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x_{1} = 1,75\ \ \ \\ y_{1} = - 2,25 \\ \end{matrix} \right.\ \text{\ \ \ }или\ \]
\[\left\{ \begin{matrix} x_{2} = - 1,75 \\ y_{2} = 2,25.\ \ \\ \end{matrix} \right.\ \]
\[Ответ:а)\ (2;1);( - 2;\ - 1);\]
\[\textbf{б)}\ ( - 1,75;2,25);(1,75;\ - 2,25)\text{.\ }\]