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Contests
National and Regional Contests
Austria Contests
Austrian MO National Competition
2019 Federal Competition For Advanced Students, P2
4
Simple inequality
Simple inequality
Source: Austria 2019
June 2, 2019
inequalities
BPSQ
High school olympiad
China
Austria
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be the positive real numbers such that
a
+
b
+
c
+
2
=
a
b
c
.
a+b+c+2=abc .
a
+
b
+
c
+
2
=
ab
c
.
Prove that
(
a
+
1
)
(
b
+
1
)
(
c
+
1
)
≥
27.
(a+1)(b+1)(c+1)\geq 27.
(
a
+
1
)
(
b
+
1
)
(
c
+
1
)
≥
27.
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