a) `x^3-16x=0`
⇔`x(x^2-16)=0`
⇔\(\left[ \begin{array}{l}x=0\\x^2-16=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=0\\x^2=16\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=0\\x=±4\end{array} \right.\)
Vậy `S={0,+-4}`
b) `x^4-2x^3+10x^2-20x=0`
⇔`(x^4-2x^3)+(10x^2-20x)=0`
⇔`x^3(x-2)+10x(x-2)=0`
⇔`x(x-2)(x^2+10)=0`
⇔\(\left[ \begin{array}{l}x=0\\x-2=0\\x^2+10=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=0\\x=2\\x^2=-10\text{(vô lý)}\end{array} \right.\)
Vậy `S={0,2}`
c) `(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`
⇔\(\left[ \begin{array}{l}x-8=0\\3x+2=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=8\\x=-\dfrac{2}{3}\end{array} \right.\)
Vậy `S={8,-2/3}`
