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Byju's Answer
Standard XII
Mathematics
Relation between AM,GM,HM for 2 Numbers
If a,b,c>0, a...
Question
If
a
,
b
,
c
>
0
,
a
b
2
c
3
=
64
and
a
+
b
+
c
=
k
,
then
A
maximum value of
k
=
3
√
3
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B
at maximum value of
k
,
a
:
b
:
c
=
3
:
2
:
1
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C
at minimum value of
k
,
a
:
b
:
c
=
1
:
2
:
3
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D
minimum value of
k
=
6
×
(
16
27
)
1
/
6
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Solution
The correct option is
D
minimum value of
k
=
6
×
(
16
27
)
1
/
6
a
+
2
⋅
b
2
+
3
⋅
c
3
6
≥
6
√
a
(
b
2
)
2
(
c
3
)
3
⇒
k
≥
6
×
6
√
64
4
×
27
=
6
×
(
16
27
)
1
/
6
So, the minimum value of
k
=
6
×
(
16
27
)
1
/
6
At this value
a
=
b
2
=
c
3
⇒
a
:
b
:
c
=
1
:
2
:
3
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Q.
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Relation between AM,GM,HM for 2 Numbers
Standard XII Mathematics
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