Difference between revisions of "2016 OIM Problems/Problem 2"
(Created page with "== Problem == Find all positive real solutions of the system of equations: <cmath>x=\frac{1}{y^2+y-1},\\y=\frac{1}{z^2+z-1},\\z=\frac{1}{x^2+x-1}</cmath> ~translated into Eng...") |
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== Problem == | == Problem == | ||
Find all positive real solutions of the system of equations: | Find all positive real solutions of the system of equations: | ||
| − | <cmath>x=\frac{1}{y^2+y-1},\ | + | <cmath>x=\frac{1}{y^2+y-1},\; y=\frac{1}{z^2+z-1},\; z=\frac{1}{x^2+x-1}</cmath> |
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
Latest revision as of 14:53, 14 December 2023
Problem
Find all positive real solutions of the system of equations:
![\[x=\frac{1}{y^2+y-1},\; y=\frac{1}{z^2+z-1},\; z=\frac{1}{x^2+x-1}\]](http://latex.artofproblemsolving.com/2/5/1/2513d4ba98934cba664f2fc82001e413254ac2ec.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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