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National and Regional Contests
Moldova Contests
Moldova National Olympiad
2010 Moldova National Olympiad
12.5
12.5
Part of
2010 Moldova National Olympiad
Problems
(1)
a infinity of triplets satisfying the relation
Source:
11/26/2010
Prove that exists a infinity of triplets
a
,
b
,
c
ā
R
a, b, c\in\mathbb{R}
a
,
b
,
c
ā
R
satisfying simultaneously the relations
a
+
b
+
c
=
0
a+b+c=0
a
+
b
+
c
=
0
and
a
4
+
b
4
+
c
4
=
50
a^4+b^4+c^4=50
a
4
+
b
4
+
c
4
=
50
.Moldova National Math Olympiad 2010, 12th grade
algebra unsolved
algebra