Question

lg^2x+lgx^2=2 help :3

Answer 1

$lg^2x+lgx^2=2; ;; ODZ:; x>0\\lg^2x+2lgx-2=0\\Zamena:; t=lgx,; ; ; t^2+2t-2=0\\D=4+8=12\\t_1=frac{-2-2sqrt3}{2}=-1-sqrt3; ; ; t_2=-1+sqrt3\\lgx=-1-sqrt3; ; Rightarrow x=10^{-1-sqrt3}\\lgx=-1+sqrt3; ; Rightarrow ; ; x=10^{-1+sqrt3}$