Question :
If one AM ‘a’ and two GM’s p and q are inserted between any two given numbers then find value of 2ASubmitted on 10/7/2024 | Answered by Vandana Rana
Answer :
Let the numbers bex
and
y
A
is their
A
.
M
.
2
A
=
x
+
y.......
(1)
Also
p
,
q
are two geometric means between
x
and
y
∴
x
,
p
,
q
,
y
are in
G
.
P
.
Since
x
,
p
,
q
are in
G
.
P
.
∴
p2
=
x
q
or x=
p2/q.......(2)
Since
p
,
q
,
y
are in
G
.
P
.
∴
q2
=
p
y
y= q2/p.....
....(3)
Adding (2)and (3)
x+y =p2/q +q2/p
x+y =( p3 +q3)/pq
put it in (1)
2A =(p3 +q3)/pq