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Home » Here, \( a = -2 \), \( b = 40 \). - Simpleprint

Here, \( a = -2 \), \( b = 40 \). - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Given \(a^2 + b^2 = 1\), the maximum of \(ab\) is \(\frac{1}{2}\) when \(a = b = \frac{\sqrt{2}}{2}\). Then:

📌 ab = \frac{1}{2} \quad \Rightarrow \quad \frac{1}{a^2} + \frac{1}{b^2} = \frac{(a^2 + b^2)^2}{a^2 b^2} = \frac{1}{(\frac{1}{2})^2} = 4

📌 Therefore, the expression becomes:

📌 Verification at \(x = \frac{\pi}{4}\) shows \(\cos x = \sin x = \frac{\sqrt{2}}{2}\), yielding:

📌 Thus, the minimum value is \(\boxed{9}\).

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