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

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

Ответ: x = arccos(-1/3) + πn, n∈Z