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2023 Myanmar IMO Training
8
3 equations with 3 (supposedly) real unknowns
3 equations with 3 (supposedly) real unknowns
Source: Own
July 15, 2023
algebra
system of equations
Problem Statement
Find all real numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
that satisfy
2
a
−
b
=
a
2
b
,
2
b
−
c
=
b
2
c
,
2
c
−
a
=
c
2
a
.
2a - b =a^2b, \qquad 2b-c = b^2 c, \qquad 2c-a= c^2 a.
2
a
−
b
=
a
2
b
,
2
b
−
c
=
b
2
c
,
2
c
−
a
=
c
2
a
.
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