Question

3^(1+2tg3x )–10* 3^(tg 3x) + 3 = 0

Answer 1

$tg3x=t \ 3^{1+2t}-10*3^t+3=0 \ 3*3^{2t}-10*3^t+3=0 \ \ 3^t=y \ 3y-10y+3=0 \ D=100-4*3*3=64=8^2 \ y_1=3;y_2=1/3 \ \ 3^t=3=>t_1=1 \ 3^t=1/3=>3^t=3^{-1}=>t_2=-1 \ \ tg3x=1=>3x= pi/4+ pi n, nin Z=>x_1= pi /12+ pi n/3,nin Z \ tg3x=-1=>3x= -pi/4+ pi k, kin Z=>x_2= -pi /12+ pi k/3,kin Z$