This week, we learn about the Arithmetic Mean-Geometric Mean Inequality, which relates the arithmetic mean and geometric mean of non-negative real values.

How would you use AM-GM to solve the following?

Given that \(a, b\) and \(c\) are positive numbers such that \(abc=1\), show that \[ \frac{a}{b} + \frac{b}{c} + \frac{c}{a} \geq a+b+c. \]

Share a problem which uses the AM-GM technique.

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