Question

Помогите, пожалуйста, с примерами$log _{2}x+log _{x}2=-2 0,15-cos2\beta; cos \beta = \sqrt[]{2}/4 cos2 \alpha =\ \textgreater \ tg^2 \alpha =1,5$

Answer 1

log2_x + logx_2 = -2;
log2_x  + 1/ log2_x = -2;
log2_x = t;
t + 1/t  = - 2;
t^2 + 2t + 1 = 0;
D = 4-4= 0;
 t = -2;

log2_x = -2;
log2_x = log2_(1/4);
 x = 1/4.

cos b= sgrt2/4;
cos 2b = 2 cos^ b - 1 = 2*(sgrt2/4)^2 - 1 = 2*2/16  - 1 = 1/4  - 1 = - 0,75;
0,15 - cos 2b= 0.15 - (-0,75) = 0,15 + 0,75 = 0,9