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Moldova Contests
Moldova Team Selection Test
2016 Moldova Team Selection Test
1
Moldova TST 2016,B1
Moldova TST 2016,B1
Source:
February 29, 2016
Moldova
Problem Statement
If
x
1
,
x
2
,
.
.
.
,
x
n
>
0
x_1,x_2,...,x_n>0
x
1
,
x
2
,
...
,
x
n
>
0
and
x
1
2
+
x
2
2
+
.
.
.
+
x
n
2
=
1
n
x_1^2+x_2^2+...+x_n^2=\dfrac{1}{n}
x
1
2
+
x
2
2
+
...
+
x
n
2
=
n
1
,prove that
∑
x
i
+
∑
1
x
i
⋅
x
i
+
1
≥
n
3
+
1.
\sum x_i+\sum \dfrac{1}{x_i \cdot x_{i+1}} \ge n^3+1.
∑
x
i
+
∑
x
i
⋅
x
i
+
1
1
≥
n
3
+
1.
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