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Byju's Answer
Standard XII
Mathematics
Integration Using Substitution
If x = 2 √3...
Question
If
x
=
2
√
3
+
2
√
2
and
(
x
+
1
x
)
2
is equal to
93
+
30
√
6
m
, then value of
m
is?
Open in App
Solution
Given,
x
=
2
√
3
+
2
√
2
.
Then,
1
x
=
1
2
√
3
+
2
√
2
=
2
√
3
−
2
√
2
(
2
√
3
+
2
√
2
)
(
2
√
3
−
2
√
2
)
=
2
√
3
−
2
√
2
(
(
4
×
3
)
−
4
√
6
+
4
√
6
−
(
4
×
2
)
)
=
2
√
3
−
2
√
2
12
−
8
=
2
(
√
3
−
√
2
)
4
.
∴
1
x
=
(
√
3
−
√
2
)
2
.
Then,
(
x
+
1
x
)
2
=
(
(
2
√
3
+
2
√
2
)
+
(
√
3
−
√
2
2
)
)
2
=
(
5
√
3
2
+
3
√
2
2
)
2
=
(
5
√
3
+
3
√
2
2
)
2
=
75
+
30
√
6
+
18
2
=
(
93
+
30
√
6
)
4
.
On comparing, the value of
m
is
4
.
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0
Similar questions
Q.
For
x
=
2
√
3
+
2
√
2
,
if
(
x
+
1
x
)
2
is
93
+
30
√
m
4
then
m
is :
Q.
If
x
=
2
√
3
+
2
√
2
and
1
x
is equal to
√
3
−
√
2
m
, then value of
m
is :
Q.
If
x
=
2
√
3
+
2
√
2
,
find :
If
x
+
1
x
is equal to
5
√
3
+
3
√
2
m
, then value of
m
is :
Q.
If
√
2
√
6
−
√
2
−
√
3
√
6
+
√
2
is equal to
2
√
3
+
2
−
3
√
2
+
√
6
m
then value of m is
Q.
If
a
2
=
log
x
,
b
3
=
log
y
and
3
a
2
−
2
b
3
=
6
log
z
, then y in terms of x and z is
y
=
x
3
2
z
m
. The value of
m
is equal to
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