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Chisinau City MO
1975 Chisinau City MO
93
Chisinau MO p93 1975 R1 IX (a^2+b^2+c^2)^2=2(a^4+b^4+c^4) if a+b+c=0
Chisinau MO p93 1975 R1 IX (a^2+b^2+c^2)^2=2(a^4+b^4+c^4) if a+b+c=0
Source:
March 16, 2021
algebra
Problem Statement
Prove that
(
a
2
+
b
2
+
c
2
)
2
=
2
(
a
4
+
b
4
+
c
4
)
(a^2 + b^2 + c^2)^ 2 = 2 (a^4 + b^4 + c^4)
(
a
2
+
b
2
+
c
2
)
2
=
2
(
a
4
+
b
4
+
c
4
)
if
a
+
b
+
c
=
0
a + b + c = 0
a
+
b
+
c
=
0
.
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