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Problems
Contests
National and Regional Contests
Greece Contests
Greece National Olympiad
2022 Greece National Olympiad
3
3
Part of
2022 Greece National Olympiad
Problems
(1)
Classical-looking inequality
Source: Greece National Olympiad 2022, Problem 3
2/26/2022
The positive real numbers
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
satisfy the equality
a
+
b
c
+
c
d
+
d
b
+
1
a
b
2
c
2
d
2
=
18.
a+bc+cd+db+\frac{1}{ab^2c^2d^2}=18.
a
+
b
c
+
c
d
+
d
b
+
a
b
2
c
2
d
2
1
=
18.
Find the maximum possible value of
a
a
a
.
Inequality
inequalities