Question

2cos2x - 12cosx + 7 = 0

Answer 1

$2cos 2x-12cos x+7=0\2(2cos^2x-1)-12cos x+7=0\4cos^2x-12cos x+5=0\D=144-4*4*5-144-80=64\cos_{1,2}x=frac{12pm 8}{8}=0,5; 2,5$

$left[begin{gathered}cos x=2,5, hfill \ cos x=0,5; \ end{gathered}\ Leftrightarrowleft[begin{gathered} xin varnothing, hfill \ x= pm frac{pi}{3}+2pi n, nin mathds{Z} \ end{gathered}\ Leftrightarrow x=pm frac{pi}{3}+2pi n, nin mathds{Z}$

$OTBET: pm frac{pi}{3}+2pi n, nin mathds{Z}$