Gọi VT = T
Đặt \(x=3a+b+c;y=3b+c+a;z=3c+a+b\)
\(\Rightarrow x+y+z=5\left(a+b+c\right)=5\left(x-2a\right)=5\left(y-2b\right)\)
\(=5\left(z-2c\right)\)
\(\Rightarrow4x-\left(y+z\right)=10a;4y-\left(z+x\right)=10b;4z-\left(x+y\right)=10c\)
\(\Rightarrow10T=\frac{4x-\left(y+z\right)}{x}+\frac{4y-\left(z+x\right)}{y}+\frac{4z-\left(x+y\right)}{z}\)
\(=12-\left(\frac{y}{x}+\frac{z}{x}+\frac{x}{y}+\frac{z}{y}+\frac{x}{z}+\frac{y}{z}\right)\le12-6=6\)
\(\Rightarrow T\le\frac{6}{10}=\frac{3}{5}\)
Dấu "=" khi a = b = c
