Задача 38977 ...

vk535418574

26 августа 2019 г. в 11:05

3. Решите неравенство

(x + 1)(x + 4)(x + 8)
──────–– ≥ –1.
(x – 1)(x – 4)(x – 8)

sova

26 августа 2019 г. в 12:44

★

(х+1)(х+4)(х+8)/(х–1)(х–4)(х–8) + 1 ≥ 0

((x+1)(x+4)(x+8)+(x–1)(x–4)(x–8) )/(x–1)(x–4)(x–8) ≥ 0

((x²+5x+4)(x+8)+(x²–5x+4)(x–8) )/(x–1)(x–4)(x–8) ≥ 0

(x³+5x²+4x+8x²+40x+32+x³–5x²+4x–8x²+40x–32 )/(x–1)(x–4)(x–8) ≥ 0

(2x³+88x)/(x–1)(x–4)(x–8) ≥ 0

2х(x²+44)/(x–1)(x–4)(x–8) ≥ 0

x/(x–1)(x–4)(x–8) ≥ 0

Применяем метод интервалов:

_+__ [0] _–_ (1) ___+___ (4) ___–___ (8) ___+___

О т в е т. (– ∞ ;0] U(1;4)U(8;+ ∞ )