\[\boxed{\text{346\ (346).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ 718x^{4} - 717x^{2} - 1 = 0\]
\[x_{1} = 1;\ \ x_{2} = - 1 \Longrightarrow корни\ \]
\[уравнения,\ находятся\ \]
\[методом\ подбора.\]
\[Схема\ Горнера:\]
\[718\] | \[0\] | \[- 717\] | \[0\] | \[- 1\] | |
---|---|---|---|---|---|
\[1\] | \[718\] | \[718\] | \[1\] | \[1\] | \[0\] |
\[- 1\] | \[718\] | \[0\] | \[1\] | \[0\] | \[0\] |
\[718x^{4} - 717x^{2} - 1 =\]
\[= (x - 1)(x + 1)\left( 718x^{2} + 1 \right)\]
\[718x^{2} + 1 > 0 \Longrightarrow x_{1} = 1;\ \]
\[\ x_{2} = - 1.\]
\[\textbf{б)}\ 206x^{4} - 205x^{2} - 1 = 0\]
\[x_{1} = 1;\ \ x_{2} = - 1 \Longrightarrow корни.\]
\[\Longrightarrow 206x^{4} - 205x^{2} - 1 =\]
\[= (x - 1)(x + 1)\left( 206x^{2} + 1 \right)\]
\[206x^{2} + 1 > 0 \Longrightarrow x_{1} = 1;\ \ \]
\[x_{2} = - 1.\]
\[Ответ:а)\ - 1;1;\ \ \ б) - 1;1.\]