1989 OIM Problems/Problem 1: Difference between revisions
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<cmath>x+y-z=-1</cmath> | <cmath>x+y-z=-1</cmath> | ||
<cmath>x^2- | <cmath>x^2-y^2+z^2=1</cmath> | ||
<cmath>-x^3+y^3+z^3=-1</cmath> | <cmath>-x^3+y^3+z^3=-1</cmath> | ||
Revision as of 17:05, 22 March 2025
Problem
Find all triples of real numbers that satisfy the system of equations:
![\[x+y-z=-1\]](http://latex.artofproblemsolving.com/4/a/a/4aa734f24b8e5bd18fb4acfcda17cc192edc8b8b.png)
![\[x^2-y^2+z^2=1\]](http://latex.artofproblemsolving.com/7/c/e/7ce715737673fdea26da5fbbcab0f9eba639a911.png)
![\[-x^3+y^3+z^3=-1\]](http://latex.artofproblemsolving.com/3/e/b/3ebeca29bdbdc7c3f91a976dd61e14705b211349.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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