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Byju's Answer
Standard XII
Mathematics
Arithmetic Progression
If a2, b2, ...
Question
If
a
2
,
b
2
,
c
2
are in A.P. then the following are also in A.P. True or False? If true write 1 otherwise write 0
a
b
+
c
,
b
c
+
a
,
c
a
+
b
.
Open in App
Solution
Assume
a
b
+
c
,
b
c
+
a
,
c
a
+
b
.
are in A.P
⇒
b
c
+
a
−
a
b
+
c
=
c
a
+
b
−
b
c
+
a
⇒
(
b
c
+
a
+
1
)
−
(
a
b
+
c
+
1
)
=
(
c
a
+
b
+
1
)
−
(
b
c
+
a
+
1
)
⇒
1
c
+
a
−
1
b
+
c
=
1
a
+
b
−
1
c
+
a
⇒
b
−
a
b
+
c
=
c
−
b
a
+
b
⇒
b
2
−
a
2
=
c
2
−
b
2
⇒
2
b
2
=
a
2
+
c
2
Hence our assumption is True.
Thus answer is 1.
Suggest Corrections
0
Similar questions
Q.
If
a
2
,
b
2
,
c
2
are in A.P., then the following are also in A.P.
1
b
+
c
,
1
c
+
a
,
1
a
+
b
.
Q.
Given a,b,c,d are in G.P then
(
a
−
d
)
2
=
(
b
−
c
)
2
+
(
c
−
a
)
2
+
(
d
−
b
)
2
.If you think this is true then write 1 otherwise write 0 ?
Q.
State True or False. If a, b, c are in A.P., then
b
+
c
,
c
+
a
,
a
+
b
are also in A.P.
Q.
If
a
2
,
b
2
,
c
2
are in A.P. then show that
1
b
+
c
,
1
c
+
a
,
1
a
+
b
are also in A.P.
Q.
1
a
,
1
b
,
1
c
are in
H
.
P
,
then the following are also in A.P.
b
+
c
,
c
+
a
,
a
+
b
If it is true, then answer will be 1 otherwise 0.
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