Question

3cos2x=7cosx. Срочно пжжжжж

Answer 1

3 ( cos^2 x -1) -7 cos x =0
3cos^2x -7 cos x -3 =0
cos x = a; 3a^2x -7a -3 = 0
D = 25
a1 = 2; cоsx =2 - корней нет
а = 1/3; cost = 1/3; x =+-arccos 1/3 +2Пn
Ответ: +-arccos 1/3 +2Пn

Answer 2

$3\cos 2x = 7\cos x \\ 3(2\cos ^{2}x - 1) - 7\cos x = 0 \\ 6\cos ^{2}x - 3 - 7\cos x = 0 \\ \cos x = t \\ 6t^{2}-7t-3=0 \\ D = 49 + 24*3 = 121 \\ \\ t_{1} = \dfrac{7 + 11}{12} = 1.5 \ ; \ \ \ t_{2} = \dfrac{7-11}{12} = -\dfrac{1}{3} \\ \\ \left[ \begin{gathered} \cos x = 1.5 \\ \cos x = -\dfrac{1}{3} \\ \end{gathered} \right. \ \ \ ; \ \left[ \begin{gathered} x \notin [-1;1] \\ x = \pm \arccos( -\dfrac{1}{3}) + 2\pi n, n \in Z \end{gathered} \right.$

Ответ: x = arccos(-1/3) + πn, n∈Z