a) $3x(x-2)-x+2=0$
$⇔ 3x(x-2)-(x-2)=0$
$⇔ (x-2)(3x-1)=0$
$⇔ \left[ \begin{array}{l}x-2=0\\3x-1=0\end{array} \right.$
$⇔ \left[ \begin{array}{l}x=2\\x=\dfrac{1}{3}\end{array} \right.$
b) $x^2(x+1)+2x(x+1)=0$
$⇔ (x+1)(x^2+2x)=0$
$⇔ (x+1).x(x+2)=0$
$⇔ \left[ \begin{array}{l}x+1=0\\x=0\\x+2=0\end{array} \right.$
$⇔ \left[ \begin{array}{l}x=-1\\x=0\\x=-2\end{array} \right.$
c) $x(x-2)-2(3-2x)=0$
$⇔ x^2-2x+4x-6=0$
$⇔ x^2+2x-6=0$
$Δ'=1+6=7 ⇒ \sqrt[]{Δ'}=\sqrt[]{7}$
Phương trình có nghiệm là:
$x_1=-2+\sqrt[]{7}$
$x_2=-2-\sqrt[]{7}$
d) $x(2x-3)-2(3-2x)=0$
$⇔ 2x^2-3x-6+2x=0$
$⇔ 2x^2-x-6=0$
$Δ=1+4.2.6=49 ⇒ \sqrt[]{Δ}=7$
Phương trình có nghiệm là:
$x_1=(1+7):4=2$
$x_2=(1-7):4=-\dfrac{3}{2}$
