Difference between revisions of "2005 OIM Problems/Problem 1"
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== See also == | == See also == | ||
[[OIM Problems and Solutions]] | [[OIM Problems and Solutions]] |
Latest revision as of 18:06, 25 March 2025
Problem
Determine all triples of real numbers that satisfy the following system of equations:
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
One can observe:
A little more manipulation and we get:
Subtract this from
To get:
Implying that or
WLOG, assume ,
So,
Implying,
Therefore, or
So, or
permutations of
and
~creativeRaven