Ta có :\left ( a+b\right )^2\geq4ab\rightarrow\frac{ab}{a+b}\leq\frac{a+b}{4} Lập luận tương tự \frac{bc}{b+c}\leq\frac{b+c}{4},\frac{ac}{a+c}\leq\frac{a+c}{4}\rightarrow \frac{ab}{a+b}+\frac{bc}{b+c}+\frac{ac}{a+c}\leq \frac{a+b+c}{2}
Ta có :
$\left ( a+b\right )^2\geq4ab\rightarrow\frac{ab}{a+b}\leq\frac{a+b}{4}
$Lập luận tương tự
$\frac{bc}{b+c}\leq\frac{b+c}{4},\frac{ac}{a+c}\leq\frac{a+c}{4}
$$\rightarrow \frac{ab}{a+b}+\frac{bc}{b+c}+\frac{ac}{a+c}\leq \frac{a+b+c}{2}
$