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Home » La somme des solutions est \( 2 + 3 = 5 \). - 500apps

La somme des solutions est \( 2 + 3 = 5 \). - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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a^2 + 2 + \frac{1}{a^2} + b^2 + 2 + \frac{1}{b^2}
Since \(a^2 + b^2 = \cos^2 x + \sin^2 x = 1\), the expression simplifi...
+ 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{...

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