Cos2X + cosX = 0

Решить уравнение

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