ГДЗ по алгебре 9 класс Макарычев Задание 360

\[\boxed{\text{360\ (360).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ 2x^{7} + x^{6} + 2x^{4} +\]

\[+ x^{3} + 2x + 1 = 0\]

\[2x\left( x^{6} + x^{3} + 1 \right) +\]

\[+ \left( x^{6} + x^{3} + 1 \right) = 0\]

\[(2x + 1)\left( x^{6} + x^{3} + 1 \right) = 0\]

\[1)\ 2x + 1 = 0\ \ \]

\[x_{1} = - \frac{1}{2} = - 0,5.\]

\[2)\ x^{6} + x^{3} + 1 = 0\]

\[Пусть\ t = x^{3};\ t^{2} = x^{6}:\ \ \]

\[t^{2} + t + 1 = 0\]

\[D = 1 - 4 < 0 \Longrightarrow корней\ нет.\]

\[Ответ:x = - 0,5.\]

\[\textbf{б)}\ x^{7} - 2x^{6} + 2x^{4} - 4x^{3} +\]

\[+ x - 2 = 0\]

\[x^{6} \cdot (x - 2) + 2x^{3}(x - 2) +\]

\[+ (x - 2) = 0\]

\[(x - 2)\left( x^{6} + 2x^{3} + 1 \right) = 0\]

\[1)\ x - 2 = 0\ \ \]

\[x_{1} = 2.\]

\[2)\ x^{6} + 2x^{3} + 1 = 0\]

\[Пусть\ \ t = x^{3};\ \ t^{2} = x^{6}:\]

\[t^{2} + 2t + 1 = 0\]

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

\[t = - 1\]

\[\Longrightarrow x^{3} = - 1\ \ \]

\[x_{2} = - 1.\]

\[Ответ: - 1;2.\]