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1974 IMO Shortlist
4
4
Part of
1974 IMO Shortlist
Problems
(1)
Prove that the least of the numbers does not exceed 1/10
Source:
9/22/2010
The sum of the squares of five real numbers
a
1
,
a
2
,
a
3
,
a
4
,
a
5
a_1, a_2, a_3, a_4, a_5
a
1
,
a
2
,
a
3
,
a
4
,
a
5
equals
1
1
1
. Prove that the least of the numbers
(
a
i
−
a
j
)
2
(a_i - a_j)^2
(
a
i
−
a
j
)
2
, where
i
,
j
=
1
,
2
,
3
,
4
,
5
i, j = 1, 2, 3, 4,5
i
,
j
=
1
,
2
,
3
,
4
,
5
and
i
≠
j
i \neq j
i
=
j
, does not exceed
1
10
.
\frac{1}{10}.
10
1
.
Inequality
polynomial
distance
minimization
optimization
IMO Shortlist