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Greece Team Selection Test
2013 Greece Team Selection Test
3
Maximum Value
Maximum Value
Source: Greek TST,2013,Pr.3
August 28, 2014
function
inequalities proposed
inequalities
Problem Statement
Find the largest possible value of
M
M
M
for which
x
1
+
y
z
x
+
y
1
+
z
x
y
+
z
1
+
x
y
z
≥
M
\frac{x}{1+\frac{yz}{x}}+\frac{y}{1+\frac{zx}{y}}+\frac{z}{1+\frac{xy}{z}}\geq M
1
+
x
yz
x
+
1
+
y
z
x
y
+
1
+
z
x
y
z
≥
M
for all
x
,
y
,
z
>
0
x,y,z>0
x
,
y
,
z
>
0
with
x
y
+
y
z
+
z
x
=
1
xy+yz+zx=1
x
y
+
yz
+
z
x
=
1
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