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\frac12 \left(2^n - 2\right) - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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Let $y = \tan^2 x$, so $\cot^2 x = \frac{1}{y}$. Then the expression b...
+ y + \frac{1}{y}
We minimize $y + \frac{1}{y}$ for $y > 0$. By AM-GM inequality:
y + \frac{1}{y} \geq 2
Equality occurs when $y = 1$, i.e., $\tan x = 1 \Rightarrow x = \frac{...
Thus, the minimum value is:
+ 2 = \boxed{9}
Question: A regular tetrahedron has three of its vertices at $(0,0,0)$...
Let the fourth vertex be $(x, y, z)$, and recall that in a regular tet...
Compute edge lengths between the known points:

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