Solutions Algebra

Prove that ab≤ 1/2(n{a^2}+(1)/(n){b^2}) for any numbers a,b and a natural number n.

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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