Moscow Middle School Math Olympiad Question. Can you prove this inequality in one minute?

This Moscow middle school math competition question doesn't look easy. However, if the AM-GM inequality is applied, the result is easy to prove.

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[Biologymus]

Although the AM-GM in known in Algebra, number theory, many of the community does not know it. It is painful to prove it without it, but pleasant and easy with induction.

[actions-speak]

By the AM-HM inequality, AM/HM >= 1, so LHS = n^2 * AM/HM >= n^2

[slavinojunepri]

This is a clever one. Thanks for sharing.

[historyisfun]

Also Cauchy schwarz solves this instantly