Question

Решить уравнение. 2cos^2x - cosx - 1 = 0

Answer 1

$displaystyle 2cos^2x-cosx-1=0\\cosx=t; |t| leq 1\\2t^2-t-1=0\\D=1+8=9\\t_{1.2}= frac{1pm 3}{4}\\t_1=1; t_2=- frac{1}{2}$

$displaystyle cosx=1; x=2 pi n; nin Z\\cosx=- frac{1}{2}; x=pm frac{2 pi }{3}+2 pi k; kin Z$