MathDB
Problems
Contests
National and Regional Contests
Iran Contests
Iran MO (3rd Round)
2006 Iran MO (3rd Round)
3
Find x,y,z
Find x,y,z
Source: Iranian National Olympiad (3rd Round) 2006
September 19, 2006
algebra
polynomial
algebra proposed
Problem Statement
Find all real
x
,
y
,
z
x,y,z
x
,
y
,
z
that
{
x
+
y
+
z
x
=
1
2
y
+
z
+
x
y
=
1
2
z
+
x
+
y
z
=
1
2
\left\{\begin{array}{c}x+y+zx=\frac12\\ \\ y+z+xy=\frac12\\ \\ z+x+yz=\frac12\end{array}\right.
⎩
⎨
⎧
x
+
y
+
z
x
=
2
1
y
+
z
+
x
y
=
2
1
z
+
x
+
yz
=
2
1
Back to Problems
View on AoPS