5. Решите уравнение: a) (4x - 3)(4x + 3) - (4x - 1)² = 3x; 6) 16с² - 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) \( 16c^2 - 49 = 0 \)
• \( (4c)^2 - 7^2 = 0 \)
• \( (4c - 7)(4c + 7) = 0 \)
• \( 4c - 7 = 0 \) или \( 4c + 7 = 0 \)
• \( c = \frac{7}{4} \) или \( c = -\frac{7}{4} \)

Ответ:

• a) \( x = 2 \)
• б) \( c = \frac{7}{4} \) или \( c = -\frac{7}{4} \)