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Problems
Contests
National and Regional Contests
Korea Contests
Korea National Olympiad
2011 Korea National Olympiad
4
Korea Second Round 2011
Korea Second Round 2011
Source: Korea Second Round 2011 #8
August 21, 2011
function
inequalities proposed
inequalities
Problem Statement
Let
x
1
,
x
2
,
⋯
,
x
25
x_1, x_2, \cdots, x_{25}
x
1
,
x
2
,
⋯
,
x
25
real numbers such that
0
≤
x
i
≤
i
(
i
=
1
,
2
,
⋯
,
25
)
0 \le x_i \le i (i=1, 2, \cdots, 25)
0
≤
x
i
≤
i
(
i
=
1
,
2
,
⋯
,
25
)
. Find the maximum value of
x
1
3
+
x
2
3
+
⋯
+
x
25
3
−
(
x
1
x
2
x
3
+
x
2
x
3
x
4
+
⋯
x
25
x
1
x
2
)
x_{1}^{3}+x_{2}^{3}+\cdots +x_{25}^{3} - ( x_1x_2x_3 + x_2x_3x_4 + \cdots x_{25}x_1x_2 )
x
1
3
+
x
2
3
+
⋯
+
x
25
3
−
(
x
1
x
2
x
3
+
x
2
x
3
x
4
+
⋯
x
25
x
1
x
2
)
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