a) (x - 1)² - (x - 2)(x + 2) = 1
⇔ (x² - 2x + 1) - (x² - 4) = 1
⇔ x² - 2x + 1 - x² + 4 = 1
⇔ -2x + 5 = 1
⇔ -2x = -4
⇔ x = 2
Vậy x = 2
b) (x - 4)² + x.(1 - x) = 12
⇔ (x² - 8x + 16) + (x - x²) = 12
⇔ x² - 8x + 16 + x - x² =12
⇔ -7x + 16 = 12
⇔ -7x = -4
⇔ x = $\frac{4}{7}$
Vậy x = $\frac{4}{7}$
d) (3x - 2)² + (x - 9)(x + 9) - 5x.(2x + 3) = 0
⇔ (9x² - 12x + 4) + (x² - 81) - (10x² + 15x) = 0
⇔ 9x² - 12x + 4 + x² - 81 - 10x² - 15x = 0
⇔ -27x - 77 = 0
⇔ -27x = 77
⇔ x = -$\frac{77}{27}$
Vậy x = -$\frac{77}{27}$