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Spain Mathematical Olympiad
2007 Spain Mathematical Olympiad
Problem 1
Problem 1
Part of
2007 Spain Mathematical Olympiad
Problems
(1)
2007 Spain Mathematical Olympiad, Problem 1
Source: Spain Mathematical Olympiad 2007
6/7/2017
Let
a
0
,
a
1
,
a
2
,
a
3
,
a
4
a_0, a_1, a_2, a_3, a_4
a
0
,
a
1
,
a
2
,
a
3
,
a
4
be five positive numbers in the arithmetic progression with a difference
d
d
d
. Prove that
a
2
3
≤
1
10
(
a
0
3
+
4
a
1
3
+
4
a
3
3
+
a
4
3
)
.
a^3_2 \leq \frac{1}{10}(a^3_0 + 4a^3_1 + 4a^3_3 + a^3_4).
a
2
3
≤
10
1
(
a
0
3
+
4
a
1
3
+
4
a
3
3
+
a
4
3
)
.
algebra
arithmetic sequence