Question

Решите уравнение: $2 cos^{2} x - 3 cos x - 2 =0$

Answer 1

Решение в прикреплённом фото.

Answer 2

$\displaystyle\bf\\2Cos^{2} x-3Cosx-2=0\\\\Cosx=m \ \ , \ \ -1\leq m\leq 1\\\\2m^{2} -3m-2=0\\\\D=(-3)^{2} -4\cdot 2\cdot (-2)=9+16=25=5^{2} \\\\\\m_{1} =\frac{3-5}{4} =-\frac{1}{2} \\\\\\m_{2} =\frac{3+5}{4} =2 > 1-neyd\\\\\\Cosx=-\frac{1}{2} \\\\\\x=\pm \ arcCos\Big(-\frac{1}{2} \Big)+2\pi n,n\in Z\\\\\\\boxed{x=\pm \ \frac{2\pi }{3} +2\pi n,n\in Z}$