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#1 2006-03-14 00:44:35

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

solutions of the system of equations

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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#2 2006-03-14 10:36:56

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

Re: solutions of the system of equations

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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#3 2006-03-14 15:58:21

ganesh
Registered: 2005-06-28
Posts: 24,241

Re: solutions of the system of equations

Jake, I can think of one certain solution set.
(A=2, B=2, C=2, D=2, E=2)

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#4 2006-03-14 17:13:13

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

Re: solutions of the system of equations

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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#5 2006-03-14 21:16:07

ganesh
Registered: 2005-06-28
Posts: 24,241

Re: solutions of the system of equations

okay, Ricky, here is another!
A = B = C = D = E = 0

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#6 2006-03-15 04:43:26

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

Re: solutions of the system of equations

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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#7 2006-03-18 04:20:41

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

Re: solutions of the system of equations

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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