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UKMT Mathematical Olympiad for Girls, 2014

Algebra Difficulty 2.0 Junior Prove it United Kingdom

Find the minimum value of

$\frac{a^2}{b} + \frac{b}{c^2} + \frac{c}{a}$

where $a$ , $b$ and $c$ are positive real numbers.

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.