Question

Решите уравнение cos2x+10cosx-11=0. помогите ПОЖАЛУЙСТА))))

Answer 1

cos2x + 10cosx - 11 = 0
cos^2 x - sin^2 x + 10 cosx - 11 = 0
cos^2 x - (1 - cos^2 x) + 10 cosx - 11 = 0
2cos^2 x + 10 cosx - 12 = 0, cos x = t
2t^2 + 10t - 12 = 0
t^2 + 5t - 6 = 0
D = 5^2 + 4*6 = 25 + 24 = 49
t1 = (-5 + 7)/2 = 2/2 = 1
t1 = (-5-7)/2 = -12/2 = -6 - лишний корень
cos x = 1
x = pin, n э Z