Cos 2x = 2cos^2 x - 1
3 + cos 2x + 3√2*cos x = 0
3 + 2cos^2 x - 1 + 3√2*cos x = 0
Замена cos x = y; -1 <= y <= 1 при любом х<br>2y^2 + 3√2*y + 2 = 0
D = 9*2 - 4*2*2 = 18 - 16 = 2
y1 = (-3√2 - √2)/4 = -√2 < -1 - не подходит.
y2 = (-3√2 + √2)/4 = -√2/2
Обратная замена y = cos x
cos x = -√2/2
x1 = 3pi/4 + 2pi*k
x2 = 5pi/4 + 2pi*n