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

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 \(d=\sqrt3\)