1. $x^{4}-2x^{3}+10x^{2}-20x=0$
⇔ $x^{3}.(x-2)+10x.(x-2)=0$
⇔ $(x-2).(x^{3}+10x)=0$
⇔ $(x-2).x.(x^{2}+10)=0$
vì $x^{2}+10 > 0$
⇔ \(\left[ \begin{array}{l}x-2=0\\x=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=2\\x=0\end{array} \right.\)
2. $x^{2}.(x-1)-4x^{2}+8x-4=0$
⇔ $x^{2}.(x-1)-4.(x^{2}-2x+1)=0$
⇔ $x^{2}.(x-1)-4.(x-1)^{2}=0$
⇔ $(x-1).[x^{2}-4.(x-1)]=0$
⇔ $(x-1).(x^{2}-4x+4)=0
⇔ $(x-1).(x-2)^{2}=0$
⇔ \(\left[ \begin{array}{l}x-1=0\\x-2=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=1\\x=2\end{array} \right.\)
3. $(2x-3)^{2}=(x+5)^{2}$
⇔ $(2x-3)^{2}-(x+5)^{2}=0$
⇔ $(2x-3-x-5).(2x-3+x+5)=0$
⇔ $(x-8).(3x+2)=0$
⇔ \(\left[ \begin{array}{l}x-8=0\\3x+2=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=8\\x=-2/3\end{array} \right.\)
4. $x^{2}+3x-18=0$
⇔ $(x-3).(x+6)=0$
⇔ \(\left[ \begin{array}{l}x-3=0\\x+6=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=3\\x=-6\end{array} \right.\)
5. $x^{3}-11x^{2}+30x=0$
⇔ $x.(x^{2}-11x+30)=0$
⇔ $x.(x-5).(x-6)=0$
⇔ \(\left[ \begin{array}{l}x=0\\\end{array} \right.\)
\(\left[ \begin{array}{l}x-5=0\\x-6=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=0\\\end{array} \right.\)
\(\left[ \begin{array}{l}x=5\\x=6\end{array} \right.\)
6. $8x^{2}+30x+7=0$
⇔ $(4x+1).(2x+7)=0$
⇔ \(\left[ \begin{array}{l}4x+1=0\\2x+7=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=-1/4\\x=-7/2\end{array} \right.\)
7. $x^{3}-5x^{2}+8x+4=0$
⇔ $x^{3}-x^{2}-4x^{2}+4x+4x-4=0$
⇔ $x^{2}.(x-1)-4x.(x-1)+4.(x-1)=0$
⇔ $(x-1).(x^{2}-4x+4)=0$
⇔ $(x-1).(x-2)^{2}=0$
⇔ \(\left[ \begin{array}{l}x-1=0\\x-2=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=1\\x=2\end{array} \right.\)
