Question

Найдите решение уравнения: cos²x = cos x + 2

Answer 1

cos^2 (x) - cos (x) -2 =0
w =cos (x)
a*w^2 +b*w +c = 0

| корень

w1 = |d -b / 2a
w2 =-|d-b/2a
d=b^2 -4*a*c
a=1 b=-1 c=-2
то w1=2 w2=-1
cos (x)=w
x=Пn+acos (w)
x=Пn+acos (w)-П ( пи )
х1=Пn+acos (w1)
x1=Пn+acos (2)
x2=Пn+acos (w2)
x2=Пn+acos(-1)
x2=Пn+П
х3=Пn+acos (w1)-П
х3=Пn-П+acos (2)
x4=Пn+acos (w2)-П
х4=Пn+acos (-1)
x4 = Пn

x1 = П
x2=-K (acos(2)) +2П-iJ (acos (2))
x3=K (acos (2))+iJ (acos (2))