\(x^5-5x^3+4x=0\)
\(x^5-x^3-4x^3+4x=0\)
\(x^3.\left(x^2-1\right)-4x\left(x^2-1\right)=0\)
\(\left(x^3-4x\right)\left(x^2-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x^3-4x=0\\x^2-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x\left(x^2-4\right)=0\\x^2=1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=0;x=\pm2\\x=\pm1\end{cases}}\)
vậy....
\(x^5-5x^3+4x=0\Leftrightarrow x\left(x^4-5x^2+4\right)=0.\)
TH1: x=0
TH2:\(x^4-5x^2+4=0\Leftrightarrow x^4-2x^2.\frac{5}{2}+\frac{25}{4}-\frac{25}{4}+4=0\)
\(\left(x^2-\frac{5}{2}\right)^2-\frac{9}{4}=0\Leftrightarrow\left(x^2-\frac{5}{2}-\frac{3}{2}\right)\left(x^2-\frac{5}{2}+\frac{3}{2}\right)=0\)
\(\Leftrightarrow\left(x^2-4\right)\left(x^2-1\right)=0\)
\(x^2-4=0\Leftrightarrow x=2\)
\(x^2-1=0\Leftrightarrow x=1\)
\(TH2:x=2,x=1\)
\(\Rightarrow x=0:1:2\)
