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How to solve this equation?

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iwannafly

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Apr 18, 2012, 1:10:51 PM4/18/12
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I have sum(w_i, i from 1 to n)=1 given,

and also I am given a set of numbers e_i, i from 1 to n.

Now I need to find a number u, such that

sum(w_i/(u - e_i)^2, i from 1 to n) ...

My questions are: are there systematic way of finding all possible
solutions u?

And is the number of solution related to n?

I am thinking of maybe for n=2, the number of solutions u is 1?

And for general n, the number of solutions u is n-1?

Thanks a lot!

iwannafly

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Apr 18, 2012, 3:24:10 PM4/18/12
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u is unconstrained... all the rest are given... thank you!

iwannafly

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Apr 18, 2012, 3:25:48 PM4/18/12
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On Apr 18, 12:10 pm, iwannafly <comtech....@gmail.com> wrote:
u is unconstrained... all the rest are given...

and yes, w_i >=0 for all i...

Thank yuo!

iwannafly

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Apr 18, 2012, 3:31:33 PM4/18/12
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> Thank yuo!- Hide quoted text -
>
> - Show quoted text -

[Edit]

Now I need to find a number u, such that

sum(w_i/(u - e_i)^2, i from 1 to n) = 1.

And I am looking for real numbers u...

Axel Vogt

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Apr 18, 2012, 4:53:05 PM4/18/12
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After your additions you want to solve for u:

Sum(w(i)/(u - e(i))^2, i = 1 .. n) = 1;

I would guess, that is a purely numerical task
where you have to provide the data.

And if w = 0 there is no solution: neither there
is a reason, that a solution exists nor that it
should be unique.

iwannafly

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Apr 19, 2012, 12:28:25 AM4/19/12
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Thanks a lot!

To help clarify further details, I am making a new thread/topic for a
slightly different formulation..

Thank you!
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