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China National Olympiad
2019 China National Olympiad
1
China Mathematical Olympiad 2019 Q1
China Mathematical Olympiad 2019 Q1
Source: Chengdu Nov 14, 2018
November 14, 2018
inequalities
China
High School Olympiads
BPSQ
Problem Statement
Let
a
,
b
,
c
,
d
,
e
≥
−
1
a,b,c,d,e\geq -1
a
,
b
,
c
,
d
,
e
≥
−
1
and
a
+
b
+
c
+
d
+
e
=
5.
a+b+c+d+e=5.
a
+
b
+
c
+
d
+
e
=
5.
Find the maximum and minimum value of
S
=
(
a
+
b
)
(
b
+
c
)
(
c
+
d
)
(
d
+
e
)
(
e
+
a
)
.
S=(a+b)(b+c)(c+d)(d+e)(e+a).
S
=
(
a
+
b
)
(
b
+
c
)
(
c
+
d
)
(
d
+
e
)
(
e
+
a
)
.
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