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Question
Mathematics
The A. M. between two positive numbers a and b is twice the G. M. between them. The ratio of the numbers is
Q. The A. M. between two positive numbers
a
and
b
is twice the G. M. between them. The ratio of the numbers is
1311
251
Sequences and Series
Report Error
A
(
2
+
3
)
:
(
2
−
3
)
25%
B
(
2
+
3
)
:
(
2
−
3
)
41%
C
(
3
+
1
)
:
(
3
−
1
)
23%
D
None of these
11%
Solution:
Given
2
ab
=
2
a
+
b
⇒
b
a
+
a
b
=
4
⇒
t
2
−
4
t
+
5
=
0
, where
b
a
=
t
∴
t
=
2
±
3
⇒
b
a
=
2
±
3
∴
b
a
=
4
−
3
(
2
±
3
)
2
=
(
2
)
2
−
(
3
)
2
(
2
±
3
)
2
∴
a
:
b
=
2
+
3
:
2
−
3
or
2
−
3
:
2
+
3