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Home » Question: What is the sum of all positive divisors of \( 360 \) that are perfect squares? - IX Labs

Question: What is the sum of all positive divisors of \( 360 \) that are perfect squares? - IX Labs

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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+ (1 + \tan^2 x) + (1 + \cot^2 x) + 2(\tan x + \cot x) = 3 + \tan^2 x...
Let $ t = \tan x + \cot x $. Then:
\tan^2 x + \cot^2 x = t^2 - 2
+ (t^2 - 2) + 2t = t^2 + 2t + 1 = (t + 1)^2
Now, $ t = \tan x + \cot x \geq 2 $ by AM-GM, with equality when $ \ta...
So minimum occurs at $ t = 2 $, giving:
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Solution: The area of the entire spherical tumor (modeled as a circle...
A_{\text{tumor}} = \pi \cdot 6^2 = 36\pi \text{ cm}^2

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