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Byju's Answer
Standard VI
Mathematics
Addition of Unlike Terms
If a, b, c ar...
Question
If a, b, c are all non-zero and a + b + c = 0, prove that
a
2
b
c
+
b
2
c
a
+
c
2
a
b
=
3
.
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Solution
Given
:
a
+
b
+
c
=
0
As
we
know
that
,
if
a
+
b
+
c
=
0
,
then
a
3
+
b
3
+
c
3
=
3
a
b
c
Therefore
,
a
3
+
b
3
+
c
3
=
3
a
b
c
Dividing
by
a
b
c
on
both
sides
,
we
get
⇒
a
3
+
b
3
+
c
3
a
b
c
=
3
a
b
c
a
b
c
⇒
a
3
a
b
c
+
b
3
a
b
c
+
c
3
a
b
c
=
3
⇒
a
2
b
c
+
b
2
a
c
+
c
2
a
b
=
3
Hence
,
a
2
b
c
+
b
2
a
c
+
c
2
a
b
=
3
.
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