Cos(π/4 - x) > √3/2
cos(x - π/4) > √3/2
- arccos(√3/2) + 2πn < x - π/4 < arccos(√3/2) + 2πn, n∈z
- π/6 + 2πn < x - π/4 < π/6 + 2πn, n∈Z
- π/6 + π/4 + 2πn < x < π/6 + π/4 + 2πn, n∈Z
π/12 + 2πn < x < (5π)/12 + 2πn, n∈Z
Решение
x/2 + 5 > 0
3x - 1 ≥ 4x
x > - 10
4x - 3x ≤ - 1
x > - 10
x ≤ - 1
x∈ (- 10 ; - 1]
X^3 - 9x^2 + 4x + 4 = x^3 - x^2 - 8x^2 + 8x - 4x + 4 = (x - 1)(x^2 - 8x - 4)
x^3 - 7x^2 + 2x + 4 = x^3 - x^2 - 6x^2 + 6x - 4x + 4 = (x - 1)(x^2 - 6x - 4)
Получаем
(x^2 - 8x - 4) / (x^2 - 6x - 4)