Question

2cos2x/2 - cos x/2 -1 =0

Answer 1

$2cos^2(x/2)-cos(x/2)-1=0\\a=cos(x/2)\\\\2a^2-a-1=0\\D=(-1)^2-4*2*(-1)=1+8=9=3^2\\a_1=(1+3)/(2*2)=4/4=1\\a_2=(1-3)/(2*2)=-2/4=-1/2\\\\cos(x/2)=1\\x/2=2 \pi n, n\in Z\\x_1=4 \pi n, n\in Z\\\\cos(x/2)=-1/2\\x/2=б( \pi - \pi/3)+2 \pi n, n\in Z\\x_2=б4 \pi /3+4 \pi n, n\in Z$