1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Geometric Mean
If sum of two...
Question
If sum of two positive numbers
a
and
b
,
where
a
>
b
is thrice their G.M. and
a
b
=
7
+
√
p
2
,
then the value of
p
is
Open in App
Solution
Given :
a
+
b
=
3
√
a
b
Squaring both sides,
a
2
+
b
2
+
2
a
b
=
9
a
b
⇒
a
2
+
b
2
=
7
a
b
Assuming
a
≠
b
≠
0
a
b
+
b
a
=
7
Taking
a
b
=
t
⇒
t
+
1
t
=
7
⇒
t
2
−
7
t
+
1
=
0
⇒
t
=
7
±
√
45
2
⇒
t
=
7
+
√
45
2
(
∵
a
>
b
⇒
a
b
>
1
)
⇒
a
b
=
7
+
√
45
2
∴
p
=
45
Suggest Corrections
5
Similar questions
Q.
If sum of two positive numbers
a
and
b
,
where
a
>
b
is thrice their G.M. and
a
b
=
7
+
√
p
2
,
then the value of
p
is
Q.
For two positive real number's
a
and
b
, If the A.M. exceeds their G.M. by
2
and the G.M. exceeds their H.M. by
8
5
, then the value of
a
+
b
is
Q.
For two positive real number's
a
and
b
, If the A.M. exceeds their G.M. by
2
and the G.M. exceeds their H.M. by
8
5
, then the value of
a
+
b
is
Q.
If the A.M of two positive number a and b (a >b) is twice their G.M, then a : b is:
Q.
If the arithmetic mean of two positive numbers a & b (a > b) is twice their G.M., then a:b is
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Explore more
Geometric Mean
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Solve
Textbooks
Question Papers
Install app