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Problems
Contests
National and Regional Contests
Iran Contests
Iran MO (3rd Round)
2005 Iran MO (3rd Round)
3
Holder
Holder
Source: Iran 2005
August 27, 2005
function
inequalities
algebra proposed
algebra
Problem Statement
Find all
α
>
0
\alpha>0
α
>
0
and
β
>
0
\beta>0
β
>
0
that for each
(
x
1
,
…
,
x
n
)
(x_1,\dots,x_n)
(
x
1
,
…
,
x
n
)
and
(
y
1
,
…
,
y
n
)
∈
R
+
n
(y_1,\dots,y_n)\in\mathbb {R^+}^n
(
y
1
,
…
,
y
n
)
∈
R
+
n
that:
(
∑
x
i
α
)
(
∑
y
i
β
)
≥
∑
x
i
y
i
(\sum x_i^\alpha)(\sum y_i^\beta)\geq\sum x_iy_i
(
∑
x
i
α
)
(
∑
y
i
β
)
≥
∑
x
i
y
i
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