a) 3x(x - 1) + x-1 = 0 b) 2( x+3) + x^2 + 3x = 0 c) (2x - 1)^2 - (3x + 1)^2 = 0 d) x^2 -2x + (x-2) = 0

Đáp án: giải dạng phức tạp

Giải thích các bước giải:

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:

\(\eqalign{ & a)\,\,3x\left( {x - 1} \right) + \left( {x - 1} \right) = 0 \cr & \Leftrightarrow \left( {x - 1} \right)\left( {3x + 1} \right) = 0 \cr & \Leftrightarrow \left[ \matrix{ x - 1 = 0 \hfill \cr 3x + 1 = 0 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{ x = 1 \hfill \cr x = {1 \over 3} \hfill \cr} \right. \cr & b)\,\,2\left( {x + 3} \right) + {x^2} + 3x = 0 \cr & \Leftrightarrow 2\left( {x + 3} \right) + x\left( {x + 3} \right) = 0 \cr & \Leftrightarrow \left( {x + 3} \right)\left( {x + 2} \right) = 0 \cr & \Leftrightarrow \left[ \matrix{ x + 3 = 0 \hfill \cr x + 2 = 0 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{ x = - 3 \hfill \cr x = - 2 \hfill \cr} \right. \cr & c)\,\,{\left( {2x - 1} \right)^2} - {\left( {3x + 1} \right)^2} = 0 \cr & \Leftrightarrow \left( {2x - 1 + 3x + 1} \right)\left( {2x - 1 - 3x - 1} \right) = 0 \cr & \Leftrightarrow 5x\left( { - x - 2} \right) = 0 \cr & \Leftrightarrow \left[ \matrix{ 5x = 0 \hfill \cr - x - 2 = 0 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{ x = 0 \hfill \cr x = - 2 \hfill \cr} \right. \cr & d)\,\,{x^2} - 2x + \left( {x - 2} \right) = 0 \cr & \Leftrightarrow x\left( {x - 2} \right) + \left( {x - 2} \right) = 0 \cr & \Leftrightarrow \left( {x - 2} \right)\left( {x + 1} \right) = 0 \cr & \Leftrightarrow \left[ \matrix{ x - 2 = 0 \hfill \cr x + 1 = 0 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{ x = 2 \hfill \cr x = - 1 \hfill \cr} \right. \cr} \)