\(\frac{ab}{c}+\frac{bc}{a}\ge2\sqrt{\frac{acb^2}{ac}}=2b\) ; \(\frac{ab}{c}+\frac{ca}{b}\ge2a\); \(\frac{bc}{a}+\frac{ca}{b}\ge2c\)
Cộng vế với vế:
\(2\left(\frac{ab}{c}+\frac{bc}{a}+\frac{ca}{b}\right)\ge2\left(a+b+c\right)\)
\(\Rightarrow\frac{ab}{c}+\frac{bc}{a}+\frac{ca}{b}\ge a+b+c\)
Dấu "=" xảy ra khi \(a=b=c\)