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2023 Greece Junior Math Olympiad
1
a+b+c=0, ab^3+bc^3+ca^3=0 , system
a+b+c=0, ab^3+bc^3+ca^3=0 , system
Source: Greece Junior Math Olympiad 2023 p1
March 2, 2024
algebra
system of equations
Problem Statement
Solve in real numbers the system:
{
a
+
b
+
c
=
0
a
b
3
+
b
c
3
+
c
a
3
=
0
\begin{cases} a+b+c=0 \\ ab^3+bc^3+ca^3=0 \end{cases}
{
a
+
b
+
c
=
0
a
b
3
+
b
c
3
+
c
a
3
=
0
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