Question

3lg^2(x-1)-10lg(x-1)+3=0

Answer 1

ОДЗ:х-1>0  x>1.
Пусть lg(x-1)=y
$3y^2-10y+3=0 \ D=100-36=64 \ y_1= frac{10-8}{2*3} = frac{2}{6} = frac{1}{3} \ \ y_2= frac{18}{6} =3 \ lg(x-1)= frac{1}{3} \ x-1=10^{ frac{1}{3} } \ x_1= sqrt[3]{10} +1; \ \ lg(x-1)=3 \ x-1=10^3 \ x_2=1001$