Question

Gọi \(x_1,x_2\left(x_1< x_2\right)\) là các nghiệm của phương trình \(log^2_{\dfrac{1}{3}}\left(x\right)-5log_3x+6=0\). Tính \(\dfrac{x_2}{x_1}\)?

Answer 1

Ta có: \(log_{\dfrac{1}{3}}^2\left(x\right)-5log_3\left(x\right)+6=0\)

\(\Leftrightarrow-log_3^2\left(x\right)-5log_3\left(x\right)+6=0\)

\(\Leftrightarrow log_3^2\left(x\right)-5log_3\left(x\right)+6=0\)

\(\Leftrightarrow\left[{}\begin{matrix}log_3\left(x\right)=3\\log_3\left(x\right)=2\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=3^3=27\\x=3^2=9\end{matrix}\right.\)

\(\Rightarrow\dfrac{x_2}{x_1}=\dfrac{27}{9}=3\)