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Solve simultaneous with linear and quintic (Posted on 2020-12-29)

Solve the system
x+y+z=1
x⁵+y⁵+z⁵=1
in real numbers.

No Solution Yet Submitted by Danish Ahmed Khan

Rating: 3.0000 (1 votes)

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First look

| Comment 1 of 4

From inspection, some individual point solutions are:
(0,1,-1), (0,-1,1), (1,0,-1), (-1,0,1), (-1,1,0), (1,-1,0)

If we use {a,b,c} as a shorthand to represent any permutation of {x,y,z}:
{a,b,c} = {0,1,-1} is one set of solutions

Also: a = 1 AND b = -c is another set of solutions

There may be more ...

Edited on December 29, 2020, 7:07 am

Posted by Larry on 2020-12-29 07:06:51

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