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National and Regional Contests
China Contests
(China) National High School Mathematics League
2016 China Second Round Olympiad
1
China Second Round Olympiad 2016 Test 2 Q1
China Second Round Olympiad 2016 Test 2 Q1
Source: Sep 11, 2016
September 11, 2016
inequalities
algebra
China
BPSQ
Problem Statement
Let
a
1
,
a
2
,
…
,
a
2016
a_1, a_2, \ldots, a_{2016}
a
1
,
a
2
,
…
,
a
2016
be real numbers such that
9
a
i
≥
11
a
i
+
1
2
9a_i\ge 11a^2_{i+1}
9
a
i
≥
11
a
i
+
1
2
(
i
=
,
2
,
⋯
,
2015
)
(i=,2,\cdots,2015)
(
i
=
,
2
,
⋯
,
2015
)
. Find the maximum value of
(
a
1
−
a
2
2
)
(
a
2
−
a
3
2
)
⋯
(
a
2015
−
a
2016
2
)
(
a
2016
−
a
1
2
)
.
(a_1-a^2_2)(a_2-a^2_3)\cdots (a_{2015}-a^2_{2016})(a_{2016}-a^2_{1}).
(
a
1
−
a
2
2
)
(
a
2
−
a
3
2
)
⋯
(
a
2015
−
a
2016
2
)
(
a
2016
−
a
1
2
)
.
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