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2016 Latvia National Olympiad 3rd Round Grade10Problem3
2016 Latvia National Olympiad 3rd Round Grade10Problem3
Source:
July 22, 2016
algebra
inequalities
Problem Statement
Assume that real numbers
x
x
x
,
y
y
y
and
z
z
z
satisfy
x
+
y
+
z
=
3
x + y + z = 3
x
+
y
+
z
=
3
. Prove that
x
y
+
x
z
+
y
z
≤
3
xy + xz + yz \leq 3
x
y
+
x
z
+
yz
≤
3
.
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