$\text{_Bài làm_}$
$a) x³-7x-6=0$
$⇔ x³+x²-x²-x-6x-6=0$
$⇔ x²(x+1)-x(x+1)-6(x+1)=0$
$⇔ (x+1)(x²-x-6)=0$
$⇔ (x+1)(x²+2x-3x-6)=0$
$⇔ (x+1)[x(x+2)-3(x+2)]=0$
$⇔ (x+1)(x+2)(x-3)=0$
$⇒ $$\left\{{{x+1=0}\atop{x+2=0}}\atop{x-3=0}\right.$
$⇔ $$\left\{{{x=-1}\atop{x=-2}}\atop{x=3}\right.$
$\text{Vậy x ∈ {-1;-2;3}}$
$b) x³+27+(x+3)(x-9)=0$
$⇔ x³+27+x²+9x+3x+27=0$
$⇔ x³+54+x²+12x=0$
$⇔ x³+x²+12x+54=0$
$⇔ x³+3x²-2x²-6x+18x+54=0$
$⇔ x²(x+3)-2x(x+3)+18(x+3)=0$
$⇔ (x+3)(x²-2x+18)=0$
$⇒ \left[ \begin{array}{l}x+3=0\\x²-2x+18=0\end{array} \right.$
$⇒ \left[ \begin{array}{l}x=-3\\x ∉ R\end{array} \right.$
$\text{Vậy x=-3}$
$c) 8x³-12x²+6x-1=0$
$⇔ (2x-1)³=0$
$⇔ 2x-1=0$
$⇔ 2x=1$
$⇔ x=\frac{1}{2} $
$\text{Vậy x=$\frac{1}{2}$}$
