[See] Prove that ab≤ 1/2(na^2+1/nb^2) for any numbers a,b and a natural number
Question: Prove that
\[ab\le \frac{1}{2}\left( n{{a}^{2}}+\frac{1}{n}{{b}^{2}} \right)\]for any numbers \(a,b\) and a natural number \(n\).
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