Tìm x biết: (x – 7)(x² – 9x + 20)(x – 2) = 72.

(x – 7)(x² – 9x + 20)(x – 2) = 72

⇔ (x² – 9x+ 20)(x² – 9x + 14) – 72 = 0

Đặt x² – 9x + 14 = a

Ta có:

(a + 6)a – 72 = 0

⇔ a² + 6a – 72 = 0

⇔ (a – 6)(a + 12) = 0

⇔$\left[\begin{array}{l}a=6\\ a=-12\end{array}\right.$

Với a = 6 thì x² – 9x + 14 = 6

⇔ x² – 9x + 8 = 0

⇔ (x – 8)(x – 1) = 0

⇔$\left[\begin{array}{l}x=1\\ x=8\end{array}\right.$

Với a = –12 thì x² – 9x + 14 = –12

⇔ x² – 9x + 26 = 0

⇔ ${\left(x-\frac{9}{2}\right)}^2+\frac{23}{4}=0$ (vô lí)

Vậy x = 1 hoặc x = 8.