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**Jake****Member**- Registered: 2006-03-14
- Posts: 2

find all positive solutions of the system of equations:

A + B = C^2

B + C = D^2

C + D = E^2

D + E = A^2

E + A = B^2

anyone know how to solve this?

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**ryos****Member**- Registered: 2005-08-04
- Posts: 394

You know, that system looks about as solved as it's ever going to get. I suppose you could take the square roots if you really wanted to, giving values for all 5 terms.

El que pega primero pega dos veces.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,071

Jake, I can think of one certain solution set.

(A=2, B=2, C=2, D=2, E=2)

Character is who you are when no one is looking.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

So is that the only solution? Or are there infinitely many?

I tried a bunch of different attempts, but have only gone in circles. Too bad we aren't doing trig...

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,071

okay, Ricky, here is another!

A = B = C = D = E = 0

Character is who you are when no one is looking.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

I've "simplified" it down into two simultaneous equations that only involve A and B. Here we go:

Have fun solving those.

Why did the vector cross the road?

It wanted to be normal.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

I'm sure that there aren't other positive solutions except (2,2,2,2,2).

But cannot prove it.

IPBLE: Increasing Performance By Lowering Expectations.

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