+ 2 = \boxed{9}

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• y + \frac{1}{y} \geq 2
• Equality occurs when $y = 1$, i.e., $\tan x = 1 \Rightarrow x = \frac{\pi}{4}$.
• Thus, the minimum value is:
• Question: A regular tetrahedron has three of its vertices at $(0,0,0)$, $(1,1,0)$, and $(1,0,1)$. Find the coordinates of the fourth vertex, assuming all coordinates are integers.
• Let the fourth vertex be $(x, y, z)$, and recall that in a regular tetrahedron, all edges have equal length.
• Compute edge lengths between the known points:

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