5. Решите уравнение: a) (4x - 3)(4x + 3) - (4x - 1)² = 3x; б) 16с² - 49 = 0.

Решение:

1. а)

   \[ (4x - 3)(4x + 3) - (4x - 1)^2 = 3x \)

   \[ (16x^2 - 9) - (16x^2 - 8x + 1) = 3x \)

   \[ 16x^2 - 9 - 16x^2 + 8x - 1 = 3x \)

   \[ 8x - 10 = 3x \)

   \[ 8x - 3x = 10 \)

   \[ 5x = 10 \)

   \[ x = 2 \)

2. б)

   \[ 16c^2 - 49 = 0 \)

   \[ 16c^2 = 49 \)

   \[ c^2 = \frac{49}{16} \)

   \[ c = \pm \sqrt{\frac{49}{16}} \)

   \[ c = \pm \frac{7}{4} \)