Let $P$ be a point on the curve $xyz^2 = 2$ in three-dimensional space.  Find the minimum distance between $P$ and the origin.
Question:
Let $P$ be a point on the curve $xyz^2 = 2$ in three-dimensional space.  Find the minimum distance between $P$ and the origin.
Answer:
Let's think step by step.

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2
Let $P$ be a point on the curve $xyz^2 = 2$ in three-dimensional space.  Find the minimum distance between $P$ and the origin.
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