ĐKXĐ: x>0
\(\log_3^2x-4\cdot\log_3x+3=0\)
=>\(\left(\log_3x\right)^2-\log_3x-3\cdot\log_3x+3=0\)
=>\(\left(\log_3x-1\right)\left(\log_3x-3\right)=0\)
=>\(\left[\begin{array}{l}\log_3x-1=0\\ \log_3x-3=0\end{array}\right.\Rightarrow\left[\begin{array}{l}\log_3x=1\\ \log_3x=3\end{array}\right.\Rightarrow\left[\begin{array}{l}x=3^1=3\\ x=3^3=27\end{array}\right.\)
\(x_1^2+x_2^2=3^2+27^2=9+729=738\)
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