ГДЗ по алгебре 9 класс Макарычев Задание 343

\[\boxed{\text{343\ (343).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ p^{3} - p^{2} = 8p - 12\]

\[p^{3} - p^{2} - 8p + 12 = 0;\ \ \ \]

\[\ p = 2 \Longrightarrow корень.\]

\[(p - 2)\left( p^{2} + p - 6 \right) = 0\]

\[p^{2} + p - 6 = 0\]

\[D = 1 + 24 = 25\]

\[p_{3,4} = \frac{- 1 \pm 5}{2} = - 3;2.\]

\[Ответ:\ - 3;2.\]

\[\textbf{б)}\ p^{3} - 3p = p^{2} + 1\]

\[p^{3} - p^{2} - 3p - 1 = 0;\ \ \]

\[p = - 1 \Longrightarrow корень.\]

\[(p + 1)\left( p^{2} - 2p - 1 \right) = 0\]

\[p^{2} - 2p - 1 = 0\]

\[D_{1} = 1 + 1 = 2\]

\[p_{2,3} = 1 \pm \sqrt{2}.\]

\[Ответ:\ - 1;1 - \sqrt{2};\ \ 1 + \sqrt{2}.\]