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2004 District Olympiad
3
1 < \sqrt{1 + \sqrt{n}} < 2
1 < \sqrt{1 + \sqrt{n}} < 2
Source: 2004 Romania District VII p3
August 15, 2024
algebra
inequalities
Problem Statement
One considers the set
A
=
{
n
∈
N
∗
∣
1
<
1
+
n
<
2
}
A = \left\{ n \in N^* \big | 1 < \sqrt{1 + \sqrt{n}} < 2 \right\}
A
=
{
n
∈
N
∗
1
<
1
+
n
<
2
}
a) Find the set
A
A
A
. b) Find the set of numbers
n
∈
A
n \in A
n
∈
A
such that
n
⋅
∣
1
−
1
+
n
∣
<
1
?
\sqrt{n} \cdot \left| 1-\sqrt{1 + \sqrt{n}}\right| <1 ?
n
⋅
1
−
1
+
n
<
1
?
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