hê hiếm khi iup đêta có $\frac{a}{b} + \frac{b}{c} \geq 2\sqrt{\frac{a}{c}}$
$tg tự \frac{b}{c} + \frac{c}{a} \geq 2 \sqrt{\frac{b}{a}}$
$\frac{c}{a}+ \frac{a}{b} \geq 2\sqrt{\frac{c}{b}}$
công theo vế ta dk
$2(\frac{a}{b} + \frac{b}{c} + \frac{c}{a}) \geq 2(\sqrt{\frac{a}{c}}+ \sqrt{\frac{b}{a}} +\sqrt{\frac{c}{b}})$
$\Leftrightarrow$ đpcm