MathDB
Problems
Contests
National and Regional Contests
Italy Contests
ITAMO
2006 ITAMO
5
5
Part of
2006 ITAMO
Problems
(1)
Inequality true for positive reals
Source: ITAMO 2006 Q5
5/8/2006
Consider the inequality
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(a_1+a_2+\dots+a_n)^2\ge 4(a_1a_2+a_2a_3+\cdots+a_na_1).
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a) Find all
n
≥
3
n\ge 3
n
≥
3
such that the inequality is true for positive reals. b) Find all
n
≥
3
n\ge 3
n
≥
3
such that the inequality is true for reals.
inequalities
algebra proposed
algebra