giải pt (x^2-9)^2=12x+1

$\displaystyle  \begin{array}{{>{\displaystyle}l}}
\left( x^{2} -9\right)^{2} =12x+1\\
\Longrightarrow x^{4} -18x^{2} +81-12x-1=0\\
\Longrightarrow x^{4} -2x^{3} +2x^{3} -4x^{2} -14x^{2} +28x-40x+80=0\\
\Longrightarrow x^{3}( x-2) +2x^{2}( x-2) -14x( x-2) -40( x-2) =0\\
\Longrightarrow ( x-2)\left( x^{3} +2x^{2} -14x-40\right) =0\\
\Longrightarrow ( x-2)\left( x^{3} -4x^{2} +6x^{2} -24x+10x-40\right) =0\\
\Longrightarrow ( x-2)\left[ x^{2}( x-4) +6x( x-4) +10( x-4)\right] =0\\
\Longrightarrow ( x-2)( x-4)\left( x^{2} +6x+10\right) =0( *)
\end{array}$
Nhận xét $\displaystyle x^{2} +6x+10=x^{2} +6x+9+1=( x+3)^{2} +1 >0\ Vx$
$\displaystyle  \begin{array}{{>{\displaystyle}l}}
( *) \Longrightarrow ( x-2)( x-4) =0\\
\Longrightarrow \left[ \begin{array}{l l}
x-2=0 & \\
x-4=0 & 
\end{array} \right. \Longrightarrow \left[ \begin{array}{l l}
x=2 & \\
x=4 & 
\end{array} \right.
\end{array}$