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| Quaint Quintic Question II (Posted on 2013-10-26) |
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Determine the all possible triplets (x,y,z) of real numbers with x ≤ y ≤ z that satisfy this system of equations:
(x + y)5 = z, and:
(y + z)5 = x, and:
(z + x)5 = y
Prove that there are no others.
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Submitted by K Sengupta
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Rating: 3.0000 (1 votes)
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Solution:
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(Hide)
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There are three triplets satisfying all the conditions of the problem. They are:
(0,0,0) and:
((1/32)1/4, (1/32)1/4, (1/32)1/4) and:
(-(1/32)1/4, -(1/32)1/4, -(1/32)1/4)
For an explanation, refer to the solution submitted by Steve Herman here.
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