1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Bonus (Unexpected) solution to lagrange equation?

  1. Jul 25, 2012 #1
    1. The problem statement, all variables and given/known data

    The lagrange equations are obtained as in the picture. I am only showing the final part of the solution, where they consider the final case of x≠y≠z.

    2. Relevant equations

    The equation at the second paragraph is obtained by subtracting: (5.34 - 5.35).

    The final equations are obtained by dividing 5.37 by (x-y) throughout, same for the other 2. (Which is ok, since x - y ≠ 0)

    3. The attempt at a solution

    I understand their method, but why can't I just do this:

    (5.34) + (5.35) + (5.36)

    3(x2 + y2 + z2) + 2λ(x + y + z) + 3μ = 0

    Using the constraints,

    3(1) + 0 + 3λ = 0

    λ = -1

    Not sure if this is a appropriate solution..

    Attached Files:

  2. jcsd
  3. Jul 25, 2012 #2


    User Avatar
    Homework Helper

    You mixed lambda with mu. μ=-1.

  4. Jul 26, 2012 #3
    I see..is it possible to prove that μ=-1 leads to the equations being inconsistent?
  5. Jul 26, 2012 #4


    User Avatar
    Homework Helper

    No, μ=-1 does not matter in the argument which proves that x,y,z can not be all different.

    Two of them can be equal and in this case, you would use μ=-1 to get λ and the possible values of x,y,z.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook