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National and Regional Contests
Korea Contests
Korea National Olympiad
2008 Korean National Olympiad
2
2008 KMO P2
2008 KMO P2
Source:
August 9, 2015
Inequality
algebra
Problem Statement
We have
x
i
>
i
x_i >i
x
i
>
i
for all
1
≤
i
≤
n
1 \le i \le n
1
≤
i
≤
n
. Find the minimum value of
(
∑
i
=
1
n
x
i
)
2
∑
i
=
1
n
x
i
2
−
i
2
\frac{(\sum_{i=1}^n x_i)^2}{\sum_{i=1}^n \sqrt{x^2_i - i^2}}
∑
i
=
1
n
x
i
2
−
i
2
(
∑
i
=
1
n
x
i
)
2
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