Áp dụng bất đẳng thức Cô-si:
\(\frac{a^2}{b^2}+\frac{b^2}{c^2}\ge\frac{2a}{c}\)
\(\frac{b^2}{c^2}+\frac{c^2}{a^2}\ge\frac{2b}{c}\)
\(\frac{c^2}{a^2}+\frac{a^2}{b^2}\ge\frac{2c}{b}\)
Cộng từng vế: \(2\left(\frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{a^2}\right)\ge\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\)
<=> \(\frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{a^2}\ge\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\)