KuOV

Verified answer

2cos²2x - 1 + 5√3(2sin²x) = 8 + 5√3
2cos²2x + 5√3(1 - cos2x) = 9 + 5√3
2cos²2x + 5√3 - 5√3cos2x = 9 + 5√3
2cos²2x  - 5√3cos2x - 9 = 0
cos2x = t
2t² - 5√3t - 9 = 0
D = 75 + 72 = 147 = (7√3)²
t = (5√3 - 7√3)/4 = - √3/2                t = (5√3 + 7√3)/4 =3√3
cos2x = - √3/2                                  cos2x = 3√3
2x = + - 5π/6 + 2πn                          нет корней
x = + - 5π/12 + πn