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Serbia JBMO TST
2023 Serbia JBMO TST
3
min and max of a^3+b^3+c^3
min and max of a^3+b^3+c^3
Source: Serbia JBMO TST 2023 P3
May 28, 2023
algebra
Problem Statement
Let
a
,
b
,
c
ā
[
0
;
1
]
a, b, c \in [0;1]
a
,
b
,
c
ā
[
0
;
1
]
be reals such that
a
b
+
b
c
+
c
a
=
1
ab+bc+ca=1
ab
+
b
c
+
c
a
=
1
. Find the minimal and maximal value of
a
3
+
b
3
+
c
3
a^3+b^3+c^3
a
3
+
b
3
+
c
3
.
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