1989 OIM Problems/Problem 1

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Problem

Find all triples of real numbers that satisfy the system of equations:

\[x+y-z=-1\] \[x^2-k^2+z^2=1\] \[-x^3+y^3+z^3=-1\]

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe4.htm