Tìm x, biết: 8x³ – 12x² + 6x – 1 = 0.

8x³ – 12x² + 6x – 1 = 0

$\Leftrightarrow$ (8x³ – 1) – (12x² – 6x) = 0

$\Leftrightarrow$ [(2x)³ – 1] – 6x(2x – 1) = 0

$\Leftrightarrow$ (2x – 1)(4x² + 2x + 1) – 6x(2x – 1) = 0

$\Leftrightarrow$ (2x – 1)(4x² + 2x + 1 – 6x) = 0

$\Leftrightarrow$ (2x – 1)(4x² – 4x + 1) = 0

$\Leftrightarrow$(2x – 1)(2x – 1)² = 0

$\Leftrightarrow$ 2x – 1 = 0

$\Leftrightarrow x = \frac{1}{2}$.

Vậy phương trình đã cho có nghiệm là: $x = \frac{1}{2}$.