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Baltic Way
2002 Baltic Way
1
Symmetric simultaneous equations
Symmetric simultaneous equations
Source: Baltic Way 2002
November 12, 2010
algebra proposed
algebra
Problem Statement
Solve the system of simultaneous equations
{
a
3
+
3
a
b
2
+
3
a
c
2
−
6
a
b
c
=
1
b
3
+
3
b
a
2
+
3
b
c
2
−
6
a
b
c
=
1
c
3
+
3
c
a
2
+
3
c
b
2
−
6
a
b
c
=
1
\begin{cases}a^3+3ab^2+3ac^2-6abc=1\\ b^3+3ba^2+3bc^2-6abc=1\\c^3+3ca^2+3cb^2-6abc=1\end{cases}
⎩
⎨
⎧
a
3
+
3
a
b
2
+
3
a
c
2
−
6
ab
c
=
1
b
3
+
3
b
a
2
+
3
b
c
2
−
6
ab
c
=
1
c
3
+
3
c
a
2
+
3
c
b
2
−
6
ab
c
=
1
in real numbers.
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