Решебник по алгебре 9 класс Макарычев Задание 482

 

\[\boxed{\text{482\ (}\text{н}\text{).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ 2x - 3y + 16 > 0\]

\[2 \cdot ( - 2) - 3 \cdot 3 + 16 > 0\]

\[- 4 - 9 + 16 > 0\]

\[3 > 0 \Longrightarrow да.\]

\[\textbf{б)}\ x^{2} + 3xy - y^{2} < 20\]

\[( - 2)^{2} + 3 \cdot ( - 2) \cdot 3 - 3^{2} < 20\]

\[4 - 18 - 9 < 20\]

\[- 23 < 20 \Longrightarrow да.\]

\[\textbf{в)}\ (x + 3)^{2} + (y - 4)^{2} < 2\]

\[( - 2 + 3)^{2} + (3 - 4)^{2} < 2\]

\[1 + 1 < 2\]

\[2 < 2 \Longrightarrow нет.\]

\[\textbf{г)}\ (x + y)(y - 8) < 1\]

\[( - 2 + 3)(3 - 8) < 1\]

\[1 \cdot ( - 5) < 1\]

\[- 5 < 1 \Longrightarrow да.\]

\[\textbf{д)}\ x^{2} + y^{2} - x - y \geq 0\]

\[( - 2)^{2} + 3^{2} + 2 - 3 \geq 0\]

\[4 + 9 - 1 \geq 0\]

\[12 \geq 0 \Longrightarrow да.\]

\[\textbf{е)}\ 3x^{2} - 5y^{2} + x - y < 11\]

\[3 \cdot ( - 2)^{2} - 5 \cdot 3^{2} - 2 - 3 < 11\]

\[12 - 45 - 5 < 11\]

\[- 38 < 11 \Longrightarrow да.\ \]

\[\boxed{\text{482\ (}\text{c}\text{).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\boxed{\text{482.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[\textbf{а)}\ x² + y² + 2x + 1 = 0\]

\[(x + 1)^{2} + y^{2} = 0\]

\[\Longrightarrow x = - 1,\ \ y = 0.\]

\[\textbf{б)}\ x² - 2x + y^{2} + 4y + 5 = 0\]

\[(x - 1)^{2} + (y + 2)^{2} = 0\]

\[\Longrightarrow x = 1,\ \ y = - 2.\]