\(x^4+9=5x\left(x^2-3\right)\)
\(\Leftrightarrow x^4-5x^3+15x+9=0\)
\(\Leftrightarrow\left(x^4-3x^3\right)-\left(2x^3-6x^2\right)-\left(6x^2-18x\right)-\left(3x-9\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x^3-2x^2-6x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left[\left(x^3+x^2\right)-\left(3x^2+3x\right)-\left(3x+3\right)\right]=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+1\right)\left(x^2-3x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+1=0\\x^2-3x-3=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+1=0\\\Delta=\left(-3\right)^2-4.\left(-3\right)=21>0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\\x=\dfrac{3+\sqrt{21}}{2}\\x=\dfrac{3-\sqrt{21}}{2}\end{matrix}\right.\)
Vậy phương trình đã cho có \(S=\left\{3;-1;\dfrac{3+\sqrt{21}}{2};\dfrac{3-\sqrt{21}}{2}\right\}\)
