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2017 USAMO
6
6
Part of
2017 USAMO
Problems
(1)
Looks Like Mount Inequality Erupted :(
Source: 2017 USAMO #6
4/20/2017
Find the minimum possible value of
a
b
3
+
4
+
b
c
3
+
4
+
c
d
3
+
4
+
d
a
3
+
4
\frac{a}{b^3+4}+\frac{b}{c^3+4}+\frac{c}{d^3+4}+\frac{d}{a^3+4}
b
3
+
4
a
+
c
3
+
4
b
+
d
3
+
4
c
+
a
3
+
4
d
given that
a
a
a
,
b
b
b
,
c
c
c
,
d
d
d
are nonnegative real numbers such that
a
+
b
+
c
+
d
=
4
a+b+c+d=4
a
+
b
+
c
+
d
=
4
.Proposed by Titu Andreescu
inequalities
AMC
USA(J)MO
USAMO(2017)
Tangent line trick
Hi