Đáp án:
\[\left[ \begin{array}{l}
x = \pm 1\\
x = \pm 5,583
\end{array} \right.\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
{x^8} + 2{x^6} - 1004{x^4} - 1005{x^2} + 2006 = 0\\
\Leftrightarrow \left( {{x^8} - {x^6}} \right) + \left( {3{x^6} - 3{x^4}} \right) - \left( {1001{x^4} - 1001{x^2}} \right) - \left( {2006{x^2} - 2006} \right) = 0\\
\Leftrightarrow {x^6}\left( {{x^2} - 1} \right) + 3{x^4}\left( {{x^2} - 1} \right) - 1001{x^2}\left( {{x^2} - 1} \right) - 2006\left( {{x^2} - 1} \right) = 0\\
\Leftrightarrow \left( {{x^2} - 1} \right)\left( {{x^6} + 3{x^4} - 1001{x^2} - 2006} \right) = 0\\
\Leftrightarrow \left( {{x^2} - 1} \right)\left[ {\left( {{x^6} + 2{x^4}} \right) + \left( {{x^4} + 2{x^2}} \right) - \left( {1003{x^2} + 2006} \right)} \right] = 0\\
\Leftrightarrow \left( {{x^2} - 1} \right)\left( {{x^2} + 2} \right)\left( {{x^4} + {x^2} - 1003} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
{x^2} - 1 = 0\\
{x^2} + 2 = 0\,\,\,\left( {vn} \right)\\
{\left( {{x^2}} \right)^2} + {x^2} - 1003 = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \pm 1\\
{x^2} = 31,174...\\
{x^2} = - 32,174...
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
x = \pm 1\\
x = \pm 5,583
\end{array} \right.
\end{array}\)
