Решите уравнение: 2 cos^2 x - 3 cos x +1 = 0

Question

Решите уравнение:

2 cos^2 x - 3 cos x +1 = 0

Answer 1

2 cos^2 x - 3 cos x +1 = 0

сosx=y

2y²-3y+1=0

D=(-3)²-4*1*2 = 9-8=1

y1=(3+1)/4=1

y2=(3-1)/4=1/2=0.5

 

cosx = 1

x=2pi n,  n є Z 

 

cosx=1/2

x=±pi/3 + 2pi n,   n єZ