Giải thích các bước giải:
$\text{ a) x³ -x² -x+1 = 0}$
$\text{⇔x² (x-1)-(x-1) =0}$
$\text{⇔(x-1) (x²-1) = 0}$
$\text{⇔$\left[\begin{matrix} x-1=0\\ x²-1=0\end{matrix}\right.$}$
$\text{⇔$\left[\begin{matrix} x=1\\ x=-1\end{matrix}\right.$}$
$\text{Vậy x∈{±1}}$
$\text{ b) (2x -3)² -(4x +1)²= 0}$
$\text{⇔ 4x² -12x +9- (16x²-8x+1)= 0}$
$\text{⇔ 4x² -12x +9- 16x²+8x-1= 0}$
$\text{⇔ -12x² - 20x + 8 =0}$
$\text{⇔ 3x² +5x -2 = 0}$
$\text{⇔ 3x² +6x - x - 2= 0}$
$\text{⇔ 3x (x+2) - (x+2) =0}$
$\text{⇔ (x+2) (3x-1) = 0}$
$\text{⇔$\left[\begin{matrix} x+2=0\\ 3x-1=0\end{matrix}\right.$}$
$\text{⇔$\left[\begin{matrix} x=-2 \\ x= $\frac{1}{3}$ \end{matrix}\right.$}$
$\text{Vậy x∈{-2; $\frac{1}{3}$}$
$\text{ c) 2(x+5) -x² - 5x= 0}$
$\text{ ⇔ x² (x-1)- (x-1) =0}$
$\text{ ⇔(x-1)- (x²-1) =0}$
$\text{ ⇔$\left[\begin{matrix} x-1=0 \\ x² -1= 0 \end{matrix}\right.$}$
$\text{⇔$\left[\begin{matrix} x=1\\ x=-1\end{matrix}\right.$}$
$\text{Vậy x∈{-1; 1}}$
