Tìm x biết: (x + 1)(6x + 8)(6x + 7)^2 = 12

Lời giải:

(x + 1)(6x + 8)(6x + 7)² = 12

6(x + 1)(6x + 8)(6x + 7)² = 12.6

(6x + 6)(6x + 8)(6x + 7)² = 72

(36x² + 84x + 48)(36x² + 84x + 49) – 72 = 0

Đặt 36x² + 84x = a

Ta có:

a(a + 1) – 72 = 0

⇔ a² + a – 72 = 0

⇔ (a – 8)(a + 9) = 0

⇔ \(\left[ \begin{array}{l}a = 8\\a = - 9\left( L \right)\end{array} \right.\)

Suy ra: 36x² + 84x = 8

⇒ 36x² + 84x – 8 = 0

⇔ \(x = \frac{{ - 7 \pm \sqrt {57} }}{6}\)