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EGMO
2019 EGMO
1
Real triples
Real triples
Source: EGMO 2019 Problem 1
April 9, 2019
algebra
equations
EGMO 2019
Problem Statement
Find all triples
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
of real numbers such that
a
b
+
b
c
+
c
a
=
1
ab + bc + ca = 1
ab
+
b
c
+
c
a
=
1
and
a
2
b
+
c
=
b
2
c
+
a
=
c
2
a
+
b
.
a^2b + c = b^2c + a = c^2a + b.
a
2
b
+
c
=
b
2
c
+
a
=
c
2
a
+
b
.
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