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Byju's Answer
Standard XII
Mathematics
Sum of n Terms
If a,b,c ar...
Question
If
a
,
b
,
c
are in A.P prove that:
(i)
(
a
−
c
)
2
=
4
(
a
−
b
)
(
b
−
c
)
Open in App
Solution
b
=
a
+
b
2
⇒
R
H
S
=
4
(
a
−
a
+
c
2
)
(
a
+
c
2
−
c
)
=
4
(
2
a
−
a
−
c
2
)
(
a
+
c
−
2
c
2
)
=
4
4
(
a
−
c
)
(
a
−
c
)
=
(
a
−
c
)
2
=
R
H
S
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Similar questions
Q.
If a, b, c are in A.P., prove that:
(i) (a − c)
2
= 4 (a − b) (b − c)
(ii) a
2
+ c
2
+ 4ac = 2 (ab + bc + ca)
(iii) a
3
+ c
3
+ 6abc = 8b
3
.
Q.
If a,b,c are in AP, prove that :
(i)
(
a
−
c
)
2
=
4
(
a
−
b
)
(
b
−
c
)
(ii)
a
2
+
c
2
+
4
a
c
=
2
(
a
b
+
b
c
+
c
a
)
Q.
If a, b, c are in A.P., then show that:
(i) a
2
(b + c), b
2
(c + a), c
2
(a + b) are also in A.P.
(ii) b + c − a, c + a − b, a + b − c are in A.P.
(iii) bc − a
2
, ca − b
2
, ab − c
2
are in A.P.
Q.
If
a
,
b
,
c
are in A.P. then prove
(
a
−
c
)
2
=
4
(
b
2
−
a
c
)
.
Q.
If
a
,
b
,
c
are in continued proportion prove that:
(i)
a
2
+
a
b
+
b
2
b
2
+
b
c
+
c
2
=
a
c
(ii)
a
2
+
b
2
+
c
2
(
a
+
b
+
c
)
2
=
a
−
b
+
c
a
+
b
+
c
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