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Homework Help: Lagrange Multiplier MethodMaking Sense of the Results

  1. Jun 8, 2010 #1
    1. The problem statement, all variables and given/known data

    I am doing this lagrange multiplier problem with 2 constraints. I have completely solved it as shown in the image below. I have found that for lambda = 1 and mu = +/- 1/2 I have that x=+/- [sqrt(2)] y=+/- [1/sqrt(2)] and z=+/- [1/sqrt(2)].

    So I am trying to figure out what points I actually have now. It seemed to me that since for x,y,z I have both a positive and negative value, I should have 2*2*2= 8 points to look at. But the solution only lists four. Am I messing this up somehow? Are there not 8 points given by the solution below? Thanks.

    TTT1.jpg
     
  2. jcsd
  3. Jun 8, 2010 #2

    Dick

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    That's pretty good. But how many of those 8 points satisfy xy=1?
     
  4. Jun 8, 2010 #3
    Ah ha. I see now. Thanks Dick! Is there a general approach to keeping track of which points are valid for all constraints? Or do you just solve the n equations for n unknowns and then back-check? I know there is probably no blanket rule.. but is that the approach more times than not?
     
  5. Jun 8, 2010 #4

    Dick

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    You've got it. No, I don't think there's any more general way than back checking. Your solutions from solving subsets of the equations may give you extraneous solutions. Just back check.
     
  6. Jun 8, 2010 #5
    Thanks a bunch! :smile:
     
  7. Jun 8, 2010 #6

    cronxeh

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  8. Jun 8, 2010 #7
    Haha! Nice one cronxeh :smile:
     
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