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IMO Shortlist
2018 IMO Shortlist
A7
A7
Part of
2018 IMO Shortlist
Problems
(1)
inequality, asymmetric, nonhomogeneous, with a 7 and a radical!
Source: IMO Shortlist 2018 A7, by Evan Chen, Taiwan
7/17/2019
Find the maximal value of
S
=
a
b
+
7
3
+
b
c
+
7
3
+
c
d
+
7
3
+
d
a
+
7
3
,
S = \sqrt[3]{\frac{a}{b+7}} + \sqrt[3]{\frac{b}{c+7}} + \sqrt[3]{\frac{c}{d+7}} + \sqrt[3]{\frac{d}{a+7}},
S
=
3
b
+
7
a
+
3
c
+
7
b
+
3
d
+
7
c
+
3
a
+
7
d
,
where
a
a
a
,
b
b
b
,
c
c
c
,
d
d
d
are nonnegative real numbers which satisfy
a
+
b
+
c
+
d
=
100
a+b+c+d = 100
a
+
b
+
c
+
d
=
100
.Proposed by Evan Chen, Taiwan
IMO Shortlist