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CentroAmerican
2011 CentroAmerican
5
5
Part of
2011 CentroAmerican
Problems
(1)
Find all possible values of x+y+z
Source: Centroamerican 2011, Problem 5
6/22/2011
If
x
x
x
,
y
y
y
,
z
z
z
are positive numbers satisfying
x
+
y
z
=
y
+
z
x
=
z
+
x
y
=
2.
x+\frac{y}{z}=y+\frac{z}{x}=z+\frac{x}{y}=2.
x
+
z
y
=
y
+
x
z
=
z
+
y
x
=
2.
Find all the possible values of
x
+
y
+
z
x+y+z
x
+
y
+
z
.
inequalities
algebra proposed
algebra