Question

PTĐTTNT

(x+1)(x+2)(x+3)(x+4) - 24

Answer 1

(x + 1)(x + 2)(x + 3)(x + 4) - 24

= [(x + 1)(x + 4)][(x + 2)(x + 3)] - 24

= (x² + 4x + x +4)(x² + 3x + 2x + 12) - 24

= (x² + 5x + 4)(x² + 5x + 12) - 24

Đặt t = x² + 5x + 8

Ta có: x² + 5x + 4 = x² + 5x + 8 - 4 (1)

x² + 5x + 12 = x² + 5x + 8 + 4 (2)

Thay t = x² + 5x + 8 vào (1) và (2), ta có:

⇒ (t - 4)(t + 4) - 24

= t² - 16 - 24

= t² - 40

= (t - \(\sqrt{40}\))(t + \(\sqrt{40}\))

= (x² + 5x + 8 - \(\sqrt{40}\))(x² + 5x + 8 + \(\sqrt{40}\))