1. x² - 6x + 8 ≥ 0
D = 36 + 64 = 100
x1 = (6-10)/2 = -2
x2 = (6 + 10)/2 = 8
Ответ: x ∈ (-∞; -2) U (8; +∞)
2. (4-x²) / (x-1) > 0
__+__(-2)__-___(1)___+____(2)_-_
Ответ: x ∈ (-∞; -2) U (1; 2)
3.
{25 - x² ≥ 0
{x+3 > 0
{x + 3 ≠1
__(-5)_____(-3)/_/_/_/_/_/(-2)/_/_/_/_/_/_/(5)__
Ответ: x ∈ (-3; -2) U (-2; 5)
4.
{-x² - x + 2 ≥ 0
{sinx > 0 => x ∈ U(k ∈ Z) (2πk, π + 2πk)
D = 1 + 8 = 9
x1 = (1 - 3)/(-2) = 1
x2 = (1 + 3)/(-2) = -2
x ∈ (-2; 1)
sin x > 0 => x ∈ (0; 1)
Ответ: x ∈ (0; 1)