回復 22# windin0420 的帖子
兩次算幾是不是這樣?
\(\begin{align}
& \left( a+b \right)+\left( b+c \right)+\left( c+a \right)\ge 3\sqrt[3]{\left( a+b \right)\left( b+c \right)\left( c+a \right)} \\
& \frac{{{\log }_{b}}a}{a+b}+\frac{{{\log }_{c}}b}{b+c}+\frac{{{\log }_{a}}c}{c+a}\ge 3\sqrt[3]{\frac{1}{\left( a+b \right)\left( b+c \right)\left( c+a \right)}} \\
& \left[ \left( a+b \right)+\left( b+c \right)+\left( c+a \right) \right]\left( \frac{{{\log }_{b}}a}{a+b}+\frac{{{\log }_{c}}b}{b+c}+\frac{{{\log }_{a}}c}{c+a} \right)\ge 9 \\
& 2\left( \frac{{{\log }_{b}}a}{a+b}+\frac{{{\log }_{c}}b}{b+c}+\frac{{{\log }_{a}}c}{c+a} \right)\ge \frac{9}{a+b+c} \\
\end{align}\)
等號同時成立於\(a=b=c\)