Question

cos2X + cosX = 0
Решить уравнение

Answer 1

cos2X + cosX = 0
2cos^2x + cosx - 1 = 0
Пусть cosx = t, t ∈ [ -1; 1]
2t^2  + t - 1 = 0
D= 1 + 4*2 = 9 = 3^2
t 1 = ( - 1 + 3)/ 4 = 2/4 = 1/2
t 2  = (-1-3)/ 4 = - 1

1) cosx = 1/2
x = ± pi/3 + 2pik. kc Z
2) cosx =  - 1
x = pi + 2pik, kc Z