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Byju's Answer
Standard XII
Mathematics
In Radius
If a, b, c ar...
Question
If a, b, c are real numbers such that
b
+
c
c
+
a
a
+
b
c
+
a
a
+
b
b
+
c
a
+
b
b
+
c
c
+
a
=
0
, then show that either
a
+
b
+
c
=
0
or
,
a
=
b
=
c
.
Open in App
Solution
Let
Δ
=
b
+
c
c
+
a
a
+
b
c
+
a
a
+
b
b
+
c
a
+
b
b
+
c
c
+
a
=
2
a
+
b
+
c
2
a
+
b
+
c
2
a
+
b
+
c
c
+
a
a
+
b
b
+
c
a
+
b
b
+
c
c
+
a
Applying
R
1
→
R
1
+
R
2
+
R
3
=
2
a
+
b
+
c
1
1
1
c
+
a
a
+
b
b
+
c
a
+
b
b
+
c
c
+
a
=
2
a
+
b
+
c
1
0
0
c
+
a
b
-
c
b
-
a
a
+
b
c
-
a
c
-
b
Applying
C
2
→
C
2
-
C
1
and
C
3
→
C
3
-
C
1
=
2
a
+
b
+
c
1
b
-
c
b
-
a
c
-
a
c
-
b
=
2
a
+
b
+
c
b
-
c
c
-
b
-
b
-
a
c
-
a
=
-
2
a
+
b
+
c
a
2
+
b
2
+
c
2
-
a
b
-
b
c
-
c
a
=
-
a
+
b
+
c
2
a
2
+
2
b
2
+
2
c
2
-
2
a
b
-
2
b
c
-
2
c
a
=
-
a
+
b
+
c
a
-
b
2
+
b
-
c
2
+
c
-
a
2
But
Δ
=
0
Given
⇒
-
a
+
b
+
c
a
-
b
2
+
b
-
c
2
+
c
-
a
2
=
0
⇒
Either
a
+
b
+
c
=
0
or
a
-
b
2
+
b
-
c
2
+
c
-
a
2
=
0
⇒
a
+
b
+
c
=
0
or
a
=
b
=
c
Hence
proved
.
Suggest Corrections
0
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