Solve-2cos-2-x-2-3cos-x-2-1-0-

Question Number 113191 by ZiYangLee last updated on 11/Sep/20

Solve {2 \cos}^{2} \frac{x}{2} + 3 \cos \frac{x}{2} + 1 = 0

Answered by bobhans last updated on 11/Sep/20

{2 q}^{2} + 3 q + 1 = 0, where q = \cos (\frac{x}{2})

(2 q + 1) (q + 1) = 0

{\begin{cases} q = - \frac{1}{2} \to \cos (\frac{x}{2}) = \cos (120 °) \\ q = - 1 \to \cos (\frac{x}{2}) = \cos (180 °) \end{cases}

Commented by ZiYangLee last updated on 11/Sep/20

Tks . . But Can i know how to solve it with

general solution ?

Commented by john santu last updated on 11/Sep/20

r e c a l l \cos x = \cos α \to x = \pm α + k . 2 π, k \in Z