a) ta có : \(x^4+3x^3-2x^2+3x+1=0\)
\(\Leftrightarrow x^4-x^3+x^2+4x^3-4x^2+4x+x^2-x+1=0\)
\(\Leftrightarrow x^2\left(x^2-x+1\right)+4x\left(x^2-x+1\right)+\left(x^2-x+1\right)=0\)
\(\Leftrightarrow\left(x^2+4x+1\right)\left(x^2-x+1\right)=0\) \(\Leftrightarrow\left[{}\begin{matrix}x^2+4x+1=0\\x^2-x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}-2+\sqrt{3}\\-2-\sqrt{3}\end{matrix}\right.\\x\in\varnothing\end{matrix}\right.\) vậy \(x=-2+\sqrt{3};x=-2-\sqrt{3}\)
b) ta có : \(x^4-2x^3-5x^2+2x+1=0\)
\(\Leftrightarrow x^4+x^3-x^2-3x^3-3x^2+3x-x^2-x+1=0\)
\(\Leftrightarrow x^2\left(x^2+x-1\right)-3x\left(x^2+x-1\right)-\left(x^2+x-1\right)=0\)
\(\Leftrightarrow\left(x^2-3x-1\right)\left(x^2+x-1\right)=0\) \(\Leftrightarrow\left[{}\begin{matrix}x^2-3x-1=0\\x^2+x-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=\dfrac{3+\sqrt{13}}{2}\\x=\dfrac{3-\sqrt{13}}{2}\end{matrix}\right.\\\left[{}\begin{matrix}x=\dfrac{-1+\sqrt{5}}{2}\\x=\dfrac{-1-\sqrt{5}}{2}\end{matrix}\right.\end{matrix}\right.\)
vậy \(x=\dfrac{3+\sqrt{13}}{2};x=\dfrac{3-\sqrt{13}}{2};x=\dfrac{-1+\sqrt{5}}{2};x=\dfrac{-1-\sqrt{5}}{2}\)
