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Problems
Contests
International Contests
Austrian-Polish
1989 Austrian-Polish Competition
1
Hard and useful
Hard and useful
Source: APMC 1989
December 17, 2005
inequalities unsolved
inequalities
Problem Statement
Show that
(
∑
i
=
1
n
x
i
y
i
z
i
)
2
≤
(
∑
i
=
1
n
x
i
3
)
(
∑
i
=
1
n
y
i
3
)
(
∑
i
=
1
n
z
i
3
)
(\sum_{i=1}^{n}x_iy_iz_i)^2 \le (\sum_{i=1}^{n}x_i^3) (\sum_{i=1}^{n}y_i^3) (\sum_{i=1}^{n}z_i^3)
(
∑
i
=
1
n
x
i
y
i
z
i
)
2
≤
(
∑
i
=
1
n
x
i
3
)
(
∑
i
=
1
n
y
i
3
)
(
∑
i
=
1
n
z
i
3
)
for any positive reals
x
i
,
y
i
,
z
i
x_i, y_i, z_i
x
i
,
y
i
,
z
i
.
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