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Bulgaria JBMO Team Selection Test
2018 Bulgaria JBMO TST
3
Weird inequality from Bulgaria JBMO TST 2017
Weird inequality from Bulgaria JBMO TST 2017
Source: Bulgaria JBMO TST 2017, Day 2, Problem 3
June 25, 2018
inequalities
Problem Statement
Prove for all positive real numbers
m
,
n
,
p
,
q
m,n,p,q
m
,
n
,
p
,
q
that
m
t
+
n
+
p
+
q
+
n
t
+
p
+
q
+
m
+
p
t
+
q
+
m
+
n
+
q
t
+
m
+
n
+
p
≥
4
5
,
\frac{m}{t+n+p+q} + \frac{n}{t+p+q+m} + \frac{p}{t+q+m+n} + \frac{q}{t+m+n+p} \geq \frac{4}{5},
t
+
n
+
p
+
q
m
+
t
+
p
+
q
+
m
n
+
t
+
q
+
m
+
n
p
+
t
+
m
+
n
+
p
q
≥
5
4
,
where
t
=
m
+
n
+
p
+
q
2
.
t=\frac{m+n+p+q}{2}.
t
=
2
m
+
n
+
p
+
q
.
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