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National and Regional Contests
Iran Contests
Iran MO (2nd Round)
1997 Iran MO (2nd round)
1
x1x2x3x4=1 - Iran NMO 1997 (Second Round) - Problem4
x1x2x3x4=1 - Iran NMO 1997 (Second Round) - Problem4
Source:
October 5, 2010
inequalities proposed
inequalities
Problem Statement
Let
x
1
,
x
2
,
x
3
,
x
4
x_1,x_2,x_3,x_4
x
1
,
x
2
,
x
3
,
x
4
be positive reals such that
x
1
x
2
x
3
x
4
=
1
x_1x_2x_3x_4=1
x
1
x
2
x
3
x
4
=
1
. Prove that:
∑
i
=
1
4
x
i
3
≥
max
{
∑
i
=
1
4
x
i
,
∑
i
=
1
4
1
x
i
}
.
\sum_{i=1}^{4}{x_i^3}\geq\max\{ \sum_{i=1}^{4}{x_i},\sum_{i=1}^{4}{\frac{1}{x_i}} \}.
i
=
1
∑
4
x
i
3
≥
max
{
i
=
1
∑
4
x
i
,
i
=
1
∑
4
x
i
1
}
.
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