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Homework Help: Lagrange Mulltipliers

  1. Oct 26, 2009 #1
    1. The problem statement, all variables and given/known data

    Find max/min using L.M of the function :

    F(x,y) = x^2 + y^2 ; xy = 1

    let G(x,y) = xy - 1

    F_x = 2x
    F_y = 2y
    G_x = y
    G_y = x

    F_x = L*G_x
    F_y = L*G_y
    G(x,y) = 1


    1) 2x = L * y
    2) 2y = L * x
    3 ) xy = 1

    Now I need to solve those equations.

    so x = LY/2 ; y = LX/2

    Then if I plug it in I get X = L^2/4 and similar for Y
    Not sure how to approach that step
     
  2. jcsd
  3. Oct 26, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    x=Ly/2 and y=Lx/2 doesn't tell you x=L^2/4. Try that again.
     
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