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2002 JBMO ShortLists
6
6
Part of
2002 JBMO ShortLists
Problems
(1)
Easy inequality with 6 numbers
Source: JBMO Shortlist 2002
11/12/2008
Let
a
1
,
a
2
,
.
.
.
,
a
6
a_1,a_2,...,a_6
a
1
,
a
2
,
...
,
a
6
be real numbers such that: a_1 \not \equal{} 0, a_1a_6 \plus{} a_3 \plus{} a_4 \equal{} 2a_2a_5 \ \mathrm{and}\ a_1a_3 \ge a_2^2 Prove that
a
4
a
6
≤
a
5
2
a_4a_6\le a_5^2
a
4
a
6
≤
a
5
2
. When does equality holds?
inequalities
inequalities proposed