[tex]\frac{a+b}{c}+\frac{c+b}{a}+\frac{a+c}{b}=\frac{a}{c}+\frac{b}{c}+\frac{c}{a}+\frac{b}{a}+\frac{a}{b}+\frac{c}{b}=(\frac{a}{b}+\frac{b}{a})+(\frac{a}{c}+\frac{c}{a})+(\frac{b}{c}+\frac{c}{b})\geq 2+2+2=6[/tex] (BĐT Cau-chy)
Dấu''='' xảy ra khi a=b=c
[tex]\frac{a+b}{c}+\frac{c+b}{a}+\frac{a+c}{b}=\frac{a}{c}+\frac{b}{c}+\frac{c}{a}+\frac{b}{a}+\frac{a}{b}+\frac{c}{b}=(\frac{a}{b}+\frac{b}{a})+(\frac{a}{c}+\frac{c}{a})+(\frac{b}{c}+\frac{c}{b})\geq 2+2+2=6[/tex] (BĐT Cau-chy)
Dấu''='' xảy ra khi a=b=c