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## Homework Statement

If a, b, c > 0, prove [tex]\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \ge 3[/tex]

## Homework Equations

## The Attempt at a Solution

I'm not so sure how to do this. Usually I would try to prove that [tex]\frac{a}{b} + \frac{b}{c} + \frac{c}{a} - 3 \ge 0[/tex] but this gets me nowhere: [tex]\frac{a^2 c + b^2 a + c^2 b - 3abc}{abc}[/tex]. I can't factorise the numerator.

I know of a similar inequality that I can prove easily using this method, which is [tex]\frac{a}{b} + \frac{b}{a} \ge 2[/tex] but the inequality above is harder for me. Please help.