MathDB
Problems
Contests
International Contests
Middle European Mathematical Olympiad
2016 Middle European Mathematical Olympiad
1
cyclic system of equations in 3 variables
cyclic system of equations in 3 variables
Source: MEMO 2016 T1
August 25, 2016
system of equations
algebra
algebra proposed
quadratics
Problem Statement
Find all triples
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
of real numbers such that
a
2
+
a
b
+
c
=
0
,
a^2 + ab + c = 0,
a
2
+
ab
+
c
=
0
,
b
2
+
b
c
+
a
=
0
,
b^2 + bc + a = 0,
b
2
+
b
c
+
a
=
0
,
c
2
+
c
a
+
b
=
0.
c^2 + ca + b = 0.
c
2
+
c
a
+
b
=
0.
Back to Problems
View on AoPS