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# Let be a point on the graph of the equation in three-dimensional space. Find the minimum possible distance between and the

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Let $$P$$ be a point on the graph of the equation $$xyz=1$$ in three-dimensional space. Find the minimum possible distance between $$P$$ and the origin.

Apr 15, 2020

#1
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Distance is given by $$d=\sqrt{x^2+y^2+z^2}$$

Symmetry dictates that x = y = z at the nearest point to the origin, so $$d=\sqrt3\times x$$

Given that $$xyz=1$$  we have $$x^3=1$$ or $$x = 1$$  so minimum distance is $$d=\sqrt3$$

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Apr 15, 2020
#2
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thank you!!