Question

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

Answer 1

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