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Junior Balkan MO
2017 Junior Balkan MO
2
Simple inequality
Simple inequality
Source: JBMO 2017, Q2
June 26, 2017
inequalities
Problem Statement
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
be positive integers such that
x
≠
y
≠
z
≠
x
x\neq y\neq z \neq x
x
=
y
=
z
=
x
.Prove that
(
x
+
y
+
z
)
(
x
y
+
y
z
+
z
x
−
2
)
≥
9
x
y
z
.
(x+y+z)(xy+yz+zx-2)\geq 9xyz.
(
x
+
y
+
z
)
(
x
y
+
yz
+
z
x
−
2
)
≥
9
x
yz
.
When does the equality hold?Proposed by Dorlir Ahmeti, Albania
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