a) x(x-5)-4x+20=0
⇒ x(x-5)-(4x-20)=0
⇒ x(x-5)-4(x-5)=0
⇒ (x-4)(x-5)=0
\(\Rightarrow\left[{}\begin{matrix}x-4=0\\x-5=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=4\\x=5\end{matrix}\right.\)
b) x(x+6)-7x-42=0
⇒x(x+6)-(7x+42)=0
⇒x(x+6)-7(x+6)=0
⇒(x-7)(x+6)=0
\(\Rightarrow\left[{}\begin{matrix}x-7=0\\x+6=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=7\\x=-6\end{matrix}\right.\)
c) x3-5x2+x-5=0
⇒ (x3-5x2)+(x-5)=0
⇒ x2(x-5)+(x-5)=0
⇒ (x2+1)(x-5)=0
\(\Rightarrow\left[{}\begin{matrix}x^2+1=0\\x-5=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x^2=-1\left(loại\right)\\x=5\end{matrix}\right.\)
d) x4-2x3+10x2-20x=0
⇒(x4-2x3)+(10x2-20x)=0
⇒x3(x-2)+10x(x-2)=0
⇒(x-2)(x3+10x)=0
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\x^3+10x=0\end{matrix}\right.\)
+) x-2=0
⇒x=2
+) x3+10x=0
⇒ x(x2+10)=0
\(\Rightarrow\left[{}\begin{matrix}x=0\\x^2+10=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x^2=-10\left(loại\right)\end{matrix}\right.\)
vậy \(x=\left\{0;2\right\}\)
