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1987 IMO Longlists
67
IMO LongList 1987 - Maximum of the expression
IMO LongList 1987 - Maximum of the expression
Source:
September 6, 2010
inequalities unsolved
inequalities
Problem Statement
If
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
are real numbers such that
a
2
+
b
2
+
c
2
+
d
2
≤
1
a^2 + b^2 + c^2 + d^2 \leq 1
a
2
+
b
2
+
c
2
+
d
2
≤
1
, find the maximum of the expression
(
a
+
b
)
4
+
(
a
+
c
)
4
+
(
a
+
d
)
4
+
(
b
+
c
)
4
+
(
b
+
d
)
4
+
(
c
+
d
)
4
.
(a + b)^4 + (a + c)^4 + (a + d)^4 + (b + c)^4 + (b + d)^4 + (c + d)^4.
(
a
+
b
)
4
+
(
a
+
c
)
4
+
(
a
+
d
)
4
+
(
b
+
c
)
4
+
(
b
+
d
)
4
+
(
c
+
d
)
4
.
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