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National and Regional Contests
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MAA AMC
USAJMO
2018 USAJMO
2
2
Part of
2018 USAJMO
Problems
(1)
Too Bad I'm Lactose Intolerant
Source: 2018 USAMO Problem 1/USAJMO Problem 2
4/18/2018
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers such that
a
+
b
+
c
=
4
a
b
c
3
a+b+c=4\sqrt[3]{abc}
a
+
b
+
c
=
4
3
ab
c
. Prove that
2
(
a
b
+
b
c
+
c
a
)
+
4
min
(
a
2
,
b
2
,
c
2
)
≥
a
2
+
b
2
+
c
2
.
2(ab+bc+ca)+4\min(a^2,b^2,c^2)\ge a^2+b^2+c^2.
2
(
ab
+
b
c
+
c
a
)
+
4
min
(
a
2
,
b
2
,
c
2
)
≥
a
2
+
b
2
+
c
2
.
2018 USAMO Problem 1
2018 USAJMO Problem 2
Inequality
homogenous
Hi