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Home » From remaining 3, choose 2 to occur once each: $\binom32 = 3$ - Abu Waleed Tea

From remaining 3, choose 2 to occur once each: $\binom32 = 3$ - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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+ 4 + \frac{1}{a^2} + \frac{1}{b^2} = 5 + \frac{1}{a^2} + \frac{1}{b^2...
We apply the AM-GM inequality to \(\frac{1}{a^2} + \frac{1}{b^2}\):
\frac{1}{a^2} + \frac{1}{b^2} \geq \frac{2}{ab}
Given \(a^2 + b^2 = 1\), the maximum of \(ab\) is \(\frac{1}{2}\) when...
ab = \frac{1}{2} \quad \Rightarrow \quad \frac{1}{a^2} + \frac{1}{b^2}...
Therefore, the expression becomes:
+ 4 = 9
Verification at \(x = \frac{\pi}{4}\) shows \(\cos x = \sin x = \frac{...
Thus, the minimum value is \(\boxed{9}\).
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