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Byju's Answer
Standard XII
Mathematics
AM,GM,HM Inequality
If x2 + 1/x...
Question
If
x
2
+
1
x
2
=
A
and
x
−
1
x
=
B
then least value of
A
B
is
A
2
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B
√
2
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C
−
√
2
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D
2
√
2
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Solution
The correct option is
B
2
√
2
A
B
=
x
2
+
1
x
2
(
x
−
1
/
x
)
=
(
x
−
1
x
)
2
+
2
(
x
−
1
/
x
)
=
(
x
−
1
x
)
+
2
(
x
−
1
x
)
=
p
+
2
p
where
p
=
x
−
1
x
≥
√
2
using
A
M
≥
G
M
.
∴
Minimum value is
2
√
2
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