SOLUTION: Find all solutions of the equation cos2x + cosx = 2 in the interval [0, 4pi]

SOLUTION: Find all solutions of the equation cos2x + cosx = 2 in the interval [0, 4pi]

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Question 683542: Find all solutions of the equation cos2x + cosx = 2 in the interval [0, 4pi]
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find all solutions of the equation cos2x + cosx = 2 in the interval [0, 4pi]
cos2x + cosx = 2
2cos^2x-1+cosx=2
2cos^2x+cosx-3=0
(2cosx+3)(cosx-1)=0
2cosx+3=0
cosx=-3/2 (reject, -1≤cosx≤1)
or
cosx-1=0
cosx=1
x=0, 2π, 4π

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