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MathLinks Contest 1st
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0153 inequalities 1st edition Round 5 p3
0153 inequalities 1st edition Round 5 p3
Source:
May 9, 2021
inequalities
1st edition
Problem Statement
Prove that if the positive reals
a
,
b
,
c
a, b, c
a
,
b
,
c
have sum
1
1
1
then the following inequality holds
(
a
b
)
5
4
+
(
b
c
)
5
4
+
(
c
a
)
5
4
<
1
4
.
(ab)^{ \frac54} + (bc)^{\frac54} + (ca)^{\frac54} < \frac14 .
(
ab
)
4
5
+
(
b
c
)
4
5
+
(
c
a
)
4
5
<
4
1
.
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