MetaMath '22 - demo

Dokažite da za sve realne brojeve $a, \, b$ i $c$ vrijedi $$\frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{a^2} \geq \frac{b}{a}+\frac{c}{b}+\frac{a}{c}.$$