Minimization Problem

[jordan]

x²y²z=1

 

Find the points on the surface given above that are closest to the origin.

 

z=x^-2y^-2

 

=>we just have to minimize D=x²+y²+(x^-2y^-2)²

 

I did this and got that all the critical numbers satisfy the equation x=y...doesn't seem right...can anyone verify or refute that?

[Karnage]

well, 1st of all, yur substitutin z from elements fo teh same equation...i dunt think it will yield anythin that way.(ex: y+r = 2 --> r= 2-y --> y+(2-y) = 2 --> 0=0?) So i dunt know if yur method is valid. Does the problem give any other information?

[Perturbation]

well, 1st of all, yur substitutin z from elements fo teh same equation...i dunt think it will yield anythin that way.(ex: y+r = 2 --> r= 2-y --> y+(2-y) = 2 --> 0=0?) So i dunt know if yur method is valid. Does the problem give any other information?

 

What he's done is used pythag to get the distance from the origin to (x, y, z) and then sub'ed in what z is from the equation for the surface.