\(VT\le\frac{1}{\sqrt[3]{9}}\left(\frac{a+2b+3+3}{3}+\frac{b+2c+3+3}{3}+\frac{c+2a+3+3}{3}\right)\)
\(=\frac{1}{\sqrt[3]{9}}.\frac{3\left(a+b+c\right)+18}{3}=\frac{9}{\sqrt[3]{9}}=\sqrt[3]{81}=3\sqrt[3]{3}\)
Dấu "=" xảy ra \(\Leftrightarrow\)\(a=b=c=1\)