Question

решить уравнение 3cos²2x+10cos2x+3=0

Answer 1

$3cos^22x+10cos2x+3=0, ; cos2x=t\3t^2+10t+3=0\frac{D}{4}: (frac{10}{2})^2-3*3=16\t_1, _2=frac{-5pm 4}{3}, quad t_1=-frac{1}{3}, quad t_2=-3;\\cos2x_1=-frac{1}{3}\2x_1=pm (pi-arccosfrac{1}{3})+2pi n\x_1=pm frac{1}{2}(pi -arccosfrac{1}{3})+pi n, ; nin Z;\\ cos2x_2=-3\cosx neq -3, quad cosx in [-1;1].$