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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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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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Jake, I can think of one certain solution set.
(A=2, B=2, C=2, D=2, E=2)
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.
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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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okay, Ricky, here is another!
A = B = C = D = E = 0
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.
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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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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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