Math Is Fun Forum

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?

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.

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El que pega primero pega dos veces.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,182

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)

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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...

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"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..."

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,182

Re: solutions of the system of equations

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

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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.

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Why did the vector cross the road?
It wanted to be normal.

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.

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IPBLE:  Increasing Performance By Lowering Expectations.