write the relation of a,b,c if a^3 + b^3 + c^3 - 3abc=0 and a+b+c is not equal to 0
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Answered by
1
Answer:
Considering that
(
a
+
b
+
c
)
3
−
(
a
3
+
b
3
+
c
3
−
3
a
b
c
)
=
3
(
a
+
b
+
c
)
(
a
b
+
b
c
+
a
c
)
then if
(
a
+
b
+
c
)
≠
0
we have
(
a
+
b
+
c
)
2
=
3
(
a
b
+
b
c
+
a
c
)
and finally
a
+
b
+
c
=
±
√
3
√
a
b
+
b
c
+
a
c
NOTE:
0
=
(
a
+
b
+
c
)
2
−
3
(
a
b
+
b
c
+
a
c
)
=
a
2
+
b
2
+
c
2
−
(
a
b
+
a
c
+
b
c
)
=
1
2
(
(
a
−
b
)
2
+
(
b
−
c
)
2
+
(
a
−
c
)
2
)
=
0
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