Решите неравенство _(sqrt(x)) | (3x)/(x-4) | 4 .

Заметим, что x > 0 , x != 1 , x != 4 . Тогда _(sqrt(x)) | (3x)/(x-4) | 4 _x (3x)/(|x-4|) 2 (ln (3x)/(|x-4|) - ln x^2)/(ln x) 0 cases x > 0 (3x - x^2|x-4|)/(|x-4|(x-1)) 0 cases cases x > 0 (3 - x|x-4|)/(|x-4|(x-1)) 0 cases [ arrayl cases x > 4 x^2 - 4x - 3 0 cases cases 0 < x < 4 (x^2 - 4x + 3)/(x - 1) 0 cases array . [ arrayl x 2 + sqrt(7) cases 0 < x < 4 ((x-1)(x-3))/(x-1) 0 cases array . [ arrayl x 2 + sqrt(7) 0 < x < 1 1 < x 3 array .

x \in (0, 1) \cup (1, 3] \cup [2 + \sqrt{7}, +\infty)