Question

Решить уравнение: 2cos^2x+sinx+1=0

Answer 1

2Cos²x + Sinx + 1 = 0
2(1 - Sin²x) + Sinx + 1 = 0
2 - 2Sin²x + Sinx + 1 = 0
2Sin²x - Sinx - 3= 0
Sinx = m ,  - 1 ≤ x ≤1
2m² - m - 3 = 0
D = (-1)² - 4 * 2 * (- 3) = 1 + 24 = 25
m₁ = (1 + √25)/4 = (1 + 5)/4 = 1,5 - не подходит
m₂ = (1 - √25)/4 = (1 - 5)/4 = - 1
Sinx = - 1
x = - π/2 + 2πn, n ∈ z