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National and Regional Contests
Moldova Contests
Moldova Team Selection Test
2005 Moldova Team Selection Test
4
largest p
largest p
Source: Moldova TST 2005
April 9, 2005
inequalities
inequalities unsolved
Problem Statement
Find the largest positive
p
p
p
(
p
>
1
p>1
p
>
1
) such, that
∀
a
,
b
,
c
∈
[
1
p
,
p
]
\forall a,b,c\in[\frac1p,p]
∀
a
,
b
,
c
∈
[
p
1
,
p
]
the following inequality takes place
9
(
a
b
+
b
c
+
c
a
)
(
a
2
+
b
2
+
c
2
)
≥
(
a
+
b
+
c
)
4
9(ab+bc+ca)(a^2+b^2+c^2)\geq(a+b+c)^4
9
(
ab
+
b
c
+
c
a
)
(
a
2
+
b
2
+
c
2
)
≥
(
a
+
b
+
c
)
4
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