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Byju's Answer
Standard IX
Mathematics
Expressing Recurring Decimal in p/q Form
If l√10+√14...
Question
If
l
√
10
+
√
14
+
√
15
+
√
21
=
√
10
−
√
14
−
√
15
+
√
21
k
,
then:
A
k
=
l
2
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B
l
=
k
2
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C
l
=
2
k
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D
l
k
=
1
2
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Solution
The correct option is
C
l
=
2
k
(C) Given,
l
√
10
+
√
14
+
√
15
+
√
21
=
√
10
−
√
14
−
√
15
−
√
21
k
⇒
l
k
=
[
(
√
10
+
√
21
)
+
(
√
14
+
√
15
)
]
=
[
(
√
10
+
√
21
)
−
(
√
14
+
√
15
)
]
=
(
√
21
+
√
10
)
2
−
(
√
15
+
√
14
)
2
=
(
31
+
2
√
210
)
−
(
29
+
2
√
210
)
=
31
+
2
√
210
−
29
−
2
√
210
=
2
⇒
l
=
2
k
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0
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The equilibrium constant for the disproportionation of
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H
g
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+
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is ...............
Given,
H
g
C
l
+
+
C
l
−
⇌
H
g
C
l
2
;
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1
=
3
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H
g
C
l
2
+
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l
−
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g
C
l
−
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2
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Q.
If
D
=
∣
∣ ∣
∣
a
1
b
1
c
1
a
2
b
2
c
2
a
3
b
3
c
3
∣
∣ ∣
∣
and
D
0
=
∣
∣ ∣
∣
k
a
1
k
b
1
k
c
1
k
a
2
k
b
2
k
c
2
k
a
3
k
b
3
k
c
3
∣
∣ ∣
∣
then show that
D
0
=
k
3
D
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