`x^4-5x^3+10x+4=0` Tìm `x`

`x^4-5x^3+10x+4=0`

`⇔x^4-2x^3-3x^3+6x^2-6x^2+12x-2x+4=0`

`⇔x^3(x-2)-3x^2(x-2)-6x(x-2)-2(x-2)=0`

`⇔(x-2)(x^3-3x^2-6x-2)=0`

`⇔(x-2)(x^3+x^2-4x^2-4x-2x-2)=0`

`⇔(x-2)[x^2(x+1)-4x(x+1)-2(x+1)]=0`

`⇔(x-2)(x+1)(x^2-4x-2)=0`

`⇔`$\left[\begin{matrix} x+1=0\\ x-2=0\\x^2-4x-2=0\end{matrix}\right.$

`⇔`$\left[\begin{matrix} x=-1\\ x=2\\x^2-4x+4-6=0\end{matrix}\right.$

`⇔`$\left[\begin{matrix} x=-1\\ x=2\\(x-2)^2=6\end{matrix}\right.$

`⇔`$\left[\begin{matrix} x=-1\\ x=2\\x-2=\sqrt{6}\\x-2=-\sqrt{6}\end{matrix}\right.$

`⇔`$\left[\begin{matrix} x=-1\\ x=2\\x=\sqrt{6}+2\\x=-\sqrt{6}+2\end{matrix}\right.$