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

1. Jul 25, 2012

### unscientific

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:

• ###### lagrange3.jpg
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2. Jul 25, 2012

### ehild

You mixed lambda with mu. μ=-1.

ehild

3. Jul 26, 2012

### unscientific

I see..is it possible to prove that μ=-1 leads to the equations being inconsistent?

4. Jul 26, 2012

### ehild

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.

ehild