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Home » a + \frac1a = 2. - iBuildNew

a + \frac1a = 2. - iBuildNew

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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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:
\text{Distance between } (0,0,0) \text{ and } (1,1,0): \sqrt{(1)^2 + (...
\text{Distance between } (0,0,0) \text{ and } (1,0,1): \sqrt{(1)^2 + 0...
\text{Distance between } (1,1,0) \text{ and } (1,0,1): \sqrt{0 + (1)^2...
So all edges are of length $\sqrt{2}$.
Let’s find $(x, y, z)$ such that its distance to each of the three poi...
Distance from $(0,0,0)$:
x^2 + y^2 + z^2 = 2

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