Difference between revisions of "1989 OIM Problems/Problem 1"
(Created page with "== Problem == Find all triples of real numbers that satisfy the system of equations: <cmath>x+y-z=-1</cmath> <cmath>x^2-k^2+z^2=1</cmath> <cmath>-x^3+y^3+z^3=-1</cmath> ==...") |
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| Line 6: | Line 6: | ||
<cmath>-x^3+y^3+z^3=-1</cmath> | <cmath>-x^3+y^3+z^3=-1</cmath> | ||
| + | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
| + | |||
| + | == See also == | ||
| + | https://www.oma.org.ar/enunciados/ibe4.htm | ||
Latest revision as of 12:29, 13 December 2023
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)
![\[x^2-k^2+z^2=1\]](http://latex.artofproblemsolving.com/5/a/f/5af37f4445e551707986170753f70d47994eaff4.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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