MathDB
Problems
Contests
International Contests
Tournament Of Towns
1994 Tournament Of Towns
(433) 3
TOT 433 1994 Autumn O S3 a^3+_b^3+c^3+d^3=a+b+c+d=
TOT 433 1994 Autumn O S3 a^3+_b^3+c^3+d^3=a+b+c+d=
Source:
June 12, 2024
algebra
system of equations
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
and
d
d
d
be real numbers such that
a
3
+
b
3
+
c
3
+
d
3
=
a
+
b
+
c
+
d
=
0
a^3+b^3+c^3+d^3=a+b+c+d=0
a
3
+
b
3
+
c
3
+
d
3
=
a
+
b
+
c
+
d
=
0
Prove that the sum of a pair of these numbers is equal to
0
0
0
.(LD Kurliandchik)
Back to Problems
View on AoPS