Tìm x biết: a) (2x + 3)(x – 4) + (x – 5)(x – 2) = (3x – 5)(x – 4). b) (8x – 3)(3x + 2) – (4x + 7)(x + 4) = (2x + 1)(5x – 1).

Lời giải

a) (2x + 3)(x – 4) + (x – 5)(x – 2) = (3x – 5)(x – 4)

⇔ 2x² – 8x + 3x – 12 + x² – 2x – 5x + 10 = 3x² – 12x – 5x + 20

⇔ –12x – 2 = – 17x + 20

⇔ 5x = 22

\( \Leftrightarrow x = \frac{{22}}{5}\)

Vậy \(x = \frac{{22}}{5}\).

b) (8x – 3)(3x + 2) – (4x + 7)(x + 4) = (2x + 1)(5x – 1)

⇔ 24x² – 9x + 16x – 6 – 4x² – 16x – 7x – 28 = 10x² – 2x + 5x – 1

⇔ 20x² – 16x – 34 = 10x² + 3x – 1

⇔ 10x² – 19x – 33 = 0

⇔ 10x² – 30x + 11x – 33 = 0

⇔ 10x(x – 3) + 11(x – 3) = 0

⇔ (10x + 11)(x – 3) = 0

\( \Leftrightarrow \left[ \begin{array}{l}10{\rm{x}} + 11 = 0\\x - 3 = 0\end{array} \right.\)

\( \Leftrightarrow \left[ \begin{array}{l}{\rm{x}} = \frac{{ - 11}}{{10}}\\x = 3\end{array} \right.\)

Vậy \(x = \frac{{ - 11}}{{10}}\) hoặc x = 3.