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2003 Greece National Olympiad
2
System of equations
System of equations
Source: Greek national M.O. 2003, Final Round,problem 2
November 15, 2011
algebra unsolved
algebra
Problem Statement
Find all real solutions of the system
{
x
2
+
y
2
−
z
(
x
+
y
)
=
2
,
y
2
+
z
2
−
x
(
y
+
z
)
=
4
,
z
2
+
x
2
−
y
(
z
+
x
)
=
8.
\begin{cases}x^2 + y^2 - z(x + y) = 2, \\ y^2 + z^2 - x(y + z) = 4, \\ z^2 + x^2 - y(z + x) = 8.\end{cases}
⎩
⎨
⎧
x
2
+
y
2
−
z
(
x
+
y
)
=
2
,
y
2
+
z
2
−
x
(
y
+
z
)
=
4
,
z
2
+
x
2
−
y
(
z
+
x
)
=
8.
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