5. Решите уравнение: a) (4x-3)(4x+3)-(4x-1)² = 3x; б) 16c2-49=0.

Решение:

a) \[ (4x - 3)(4x + 3) - (4x - 1)^2 = 3x \] \[ (16x^2 - 9) - (16x^2 - 8x + 1) = 3x \] \[ 16x^2 - 9 - 16x^2 + 8x - 1 = 3x \] \[ 8x - 10 = 3x \] \[ 5x = 10 \] \[ x = 2 \] б) \[ 16c^2 - 49 = 0 \] \[ 16c^2 = 49 \] \[ c^2 = \frac{49}{16} \] \[ c = \pm \sqrt{\frac{49}{16}} \] \[ c = \pm \frac{7}{4} \]

Ответ:

• а) \[ x = 2 \]
• б) \[ c = \pm \frac{7}{4} \]

Ответ:

• а) \[ x = 2 \]
• б) \[ c = \pm \frac{7}{4} \]