MathDB
Problems
Contests
National and Regional Contests
Poland Contests
Polish MO Finals
2022 Polish MO Finals
4
Boring system of equations
Boring system of equations
Source: Poland 73-3-4
March 31, 2022
algebra
system of equations
Problem Statement
Find all triples
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
of real numbers satisfying the system
{
a
3
+
b
2
c
=
a
c
b
3
+
c
2
a
=
b
a
c
3
+
a
2
b
=
c
b
\begin{cases} a^3+b^2c=ac \\ b^3+c^2a=ba \\ c^3+a^2b=cb \end{cases}
⎩
⎨
⎧
a
3
+
b
2
c
=
a
c
b
3
+
c
2
a
=
ba
c
3
+
a
2
b
=
c
b
Back to Problems
View on AoPS