\(x^4-8x^3+6x^2+24x+9=0\)
\(\Leftrightarrow\left(x^4-6x^3-3x^2\right)+\left(-2x^3+12x^2+6x\right)+\left(-3x^2+18x+9\right)=0\)
\(\Leftrightarrow x^2\left(x^2-6x-3\right)-2x\left(x^2-6x-3\right)-3\left(x^2-6x-3\right)=0\)
\(\Leftrightarrow\left(x^2-6x-3\right)\left(x^2-2x-3\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-3\right)\left(x^2-6x-3\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x+1=0\\x-3=0\\x^2-6x-3=0\end{array}\right.\) \(\Leftrightarrow\left[\begin{array}{nghiempt}x=-1\\x=3\\x=3+2\sqrt{3}\\x=3-2\sqrt{3}\end{array}\right.\)
Vậy tập nghiệm của phương trình : \(S=\left\{-1;3-2\sqrt{3};3;3+2\sqrt{3}\right\}\)
