Đáp án:
a) x=1, x=1/3
b) x=-3, x=-2
c) x=0, x=-2
d) x=2, x=-1.
Giải thích các bước giải:
\(\eqalign{
& a)\,\,3x\left( {x - 1} \right) + \left( {x - 1} \right) = 0 \cr
& \Leftrightarrow \left( {x - 1} \right)\left( {3x + 1} \right) = 0 \cr
& \Leftrightarrow \left[ \matrix{
x - 1 = 0 \hfill \cr
3x + 1 = 0 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{
x = 1 \hfill \cr
x = {1 \over 3} \hfill \cr} \right. \cr
& b)\,\,2\left( {x + 3} \right) + {x^2} + 3x = 0 \cr
& \Leftrightarrow 2\left( {x + 3} \right) + x\left( {x + 3} \right) = 0 \cr
& \Leftrightarrow \left( {x + 3} \right)\left( {x + 2} \right) = 0 \cr
& \Leftrightarrow \left[ \matrix{
x + 3 = 0 \hfill \cr
x + 2 = 0 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{
x = - 3 \hfill \cr
x = - 2 \hfill \cr} \right. \cr
& c)\,\,{\left( {2x - 1} \right)^2} - {\left( {3x + 1} \right)^2} = 0 \cr
& \Leftrightarrow \left( {2x - 1 + 3x + 1} \right)\left( {2x - 1 - 3x - 1} \right) = 0 \cr
& \Leftrightarrow 5x\left( { - x - 2} \right) = 0 \cr
& \Leftrightarrow \left[ \matrix{
5x = 0 \hfill \cr
- x - 2 = 0 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{
x = 0 \hfill \cr
x = - 2 \hfill \cr} \right. \cr
& d)\,\,{x^2} - 2x + \left( {x - 2} \right) = 0 \cr
& \Leftrightarrow x\left( {x - 2} \right) + \left( {x - 2} \right) = 0 \cr
& \Leftrightarrow \left( {x - 2} \right)\left( {x + 1} \right) = 0 \cr
& \Leftrightarrow \left[ \matrix{
x - 2 = 0 \hfill \cr
x + 1 = 0 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{
x = 2 \hfill \cr
x = - 1 \hfill \cr} \right. \cr} \)
