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Contests
National and Regional Contests
Greece Contests
Greece JBMO TST
2009 Greece JBMO TST
4
4
Part of
2009 Greece JBMO TST
Problems
(1)
x+y+z=xy+yz+zx and xyz=1 , x,y,z>0 with min sum
Source: Greece JBMO TST 2009 p4
4/29/2019
Find positive real numbers
x
,
y
,
z
x,y,z
x
,
y
,
z
that are solutions of the system
x
+
y
+
z
=
x
y
+
y
z
+
z
x
x+y+z=xy+yz+zx
x
+
y
+
z
=
x
y
+
yz
+
z
x
and
x
y
z
=
1
xyz=1
x
yz
=
1
, and have the smallest possible sum.
algebra
system of equations
minimum
Sum