Question 179
Five positive reals $a$, $b$, $c$, $d$ and $e$ having product equal to $1$ are given. Prove that
$$
\frac{a^2}{b^2} + \frac{b^2}{c^2} + \frac{c^2}{d^2} + \frac{d^2}{e^2} + \frac{e^2}{a^2} \geq a + b + c + d + e.
$$
$$
\frac{a^2}{b^2} + \frac{b^2}{c^2} + \frac{c^2}{d^2} + \frac{d^2}{e^2} + \frac{e^2}{a^2} \geq a + b + c + d + e.
$$