\(x^4-2x^3+4x^2-3x+2=0\)
\(\Leftrightarrow x^4-2x^3+x^2+3x^2-3x+\dfrac{9}{4}-1=0\)
\(\Leftrightarrow\left(x^2-x\right)^2+3\left(x^2-x\right)+\dfrac{9}{4}-1=0\)
\(\Leftrightarrow\left(x^2-x+\dfrac{3}{2}\right)^2-1=0\)
\(\Leftrightarrow\left(x^2-x+\dfrac{3}{2}\right)^2=1\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-x+\dfrac{3}{2}=1\\x^2-x+\dfrac{3}{2}=-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-x+\dfrac{1}{4}+\dfrac{5}{4}=1\\x^2-x+\dfrac{1}{4}+\dfrac{5}{4}=-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-\dfrac{1}{2}\right)^2+\dfrac{5}{4}=1\\\left(x-\dfrac{1}{2}\right)^2+\dfrac{5}{4}=-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-\dfrac{1}{2}\right)^2=-\dfrac{1}{4}\\\left(x-\dfrac{1}{2}\right)^2=-\dfrac{9}{4}\end{matrix}\right.\)
\(\Rightarrow\) Vô lý ( vì \(\left(x-\dfrac{1}{2}\right)^2\ge0\forall x\) )
\(\Rightarrow PT\) vô nghiệm .
