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National and Regional Contests
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France Pre-TST
2005 France Pre-TST
4
French pre-TST-2004/2005 #4
French pre-TST-2004/2005 #4
Source: Me
December 20, 2004
inequalities
Problem Statement
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
be positive real numbers such that
x
2
+
y
2
+
z
2
=
25.
x^2+y^2+z^2 = 25.
x
2
+
y
2
+
z
2
=
25.
Find the minimum of
x
y
z
+
y
z
x
+
z
x
y
.
\frac {xy} z + \frac {yz} x + \frac {zx} y .
z
x
y
+
x
yz
+
y
z
x
.
Pierre.
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