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Contests
National and Regional Contests
Russia Contests
Saint Petersburg Mathematical Olympiad
2017 Saint Petersburg Mathematical Olympiad
5
Simple inequality
Simple inequality
Source: St. Petersburg 2017
August 18, 2017
inequalities
Problem Statement
Let
x
,
y
,
z
>
0
x,y,z>0
x
,
y
,
z
>
0
and
x
y
z
=
x
y
+
y
z
+
z
x
\sqrt{xyz}=xy+yz+zx
x
yz
=
x
y
+
yz
+
z
x
. Prove that
x
+
y
+
z
≤
1
3
.
x+y+z\leq \frac{1}{3}.
x
+
y
+
z
≤
3
1
.
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