ap,aq=? (a) ap×q (b) ap+q (c) (ap)2 (d) none of the above
Answers
Answered by
0
Step-by-step explanation:
a,b,c are in A.P
∴2b=a+c ______ (1) ∴b=
2
a+c
p,q,r in H.P
∴
p
1
+
r
1
=
q
2
______ (2) ∴q=
r+p
2pr
ap, bq, cr in C.P
(bq)
2
=(ap)(rc) ________ (3)
putting b and q from (1) and (2) in (3)
[(
2
a+c
)(
r+p
2pr
)]
2
=aprc
(r+p)
2
(a+c)
2
×p
2
r
2
=aprc
∴
(r+p)
2
pr
=
(a+c)
2
ac
∴
ac
a
2
+2ac+c
2
=
pr
r
2
+2rp+p
2
∴
ac
a
2
+
ac
2ac
+
ac
c
2
=
pr
r
2
+
rp
2rp
+
rp
p
2
c
a
+
a
c
=
p
r
+
r
p
LHS=RHS
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Answer:
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