Решебник по алгебре 9 класс Макарычев Задание 346

 

\[\boxed{\text{346\ (346).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ 718x^{4} - 717x^{2} - 1 = 0\]

\[x_{1} = 1;\ \ x_{2} = - 1 \Longrightarrow корни\ \]

\[уравнения,\ находятся\ \]

\[методом\ подбора.\]

\[Схема\ Горнера:\]

\[718x^{4} - 717x^{2} - 1 =\]

\[= (x - 1)(x + 1)\left( 718x^{2} + 1 \right)\]

\[718x^{2} + 1 > 0 \Longrightarrow x_{1} = 1;\ \]

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

\[\textbf{б)}\ 206x^{4} - 205x^{2} - 1 = 0\]

\[x_{1} = 1;\ \ x_{2} = - 1 \Longrightarrow корни.\]

\[\Longrightarrow 206x^{4} - 205x^{2} - 1 =\]

\[= (x - 1)(x + 1)\left( 206x^{2} + 1 \right)\]

\[206x^{2} + 1 > 0 \Longrightarrow x_{1} = 1;\ \ \]

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

\[Ответ:а)\ - 1;1;\ \ \ б) - 1;1.\]

\[\boxed{\text{346.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[x^{2} + 6x - 7 \leq 0\]

\[D = 3^{2} + 7 = 16\]

\[x_{1,2} = - 3 \pm 4\]

\[(x + 7)(x - 1) \leq 0 \Longrightarrow\]

\[\Longrightarrow x \in \lbrack - 7;1\rbrack;\]

\[x^{2} - 2x - 15 \leq 0\]

\[D = 1 + 15 = 16\]

\[x_{1,2} = 1 \pm 4\]

\[(x + 3)(x - 1) \leq 0 \Longrightarrow\]

\[\Longrightarrow x \in \lbrack - 3;1\rbrack.\]

\[Общее\ решение:\ x \in \lbrack - 3;1\rbrack.\]