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Byju's Answer
Standard XII
Mathematics
Algebra of Complex Numbers
Solution set ...
Question
Solution set of the inequation
(
x
−
√
1
−
|
x
|
)
<
0
, is
A
[
−
1
,
−
1
+
√
5
2
)
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B
[
−
1
,
1
]
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C
[
−
1
,
−
1
+
√
5
2
]
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D
(
−
1
,
−
1
+
√
5
2
)
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Solution
The correct option is
C
[
−
1
,
−
1
+
√
5
2
)
Given,
x
−
√
1
+
|
x
|
<
0
⇒
x
<
√
1
−
|
x
|
⇒
∣
∣
x
2
∣
∣
<
1
for
x
>
0
x
2
<
1
−
|
x
|
=
1
−
x
.
⇒
x
2
+
x
−
1
<
0
⇒
x
=
−
1
±
√
1
−
4
(
−
1
)
2
=
−
1
+
√
5
2
...(1)
And
√
1
−
|
x
|
is defined where
1
−
|
x
|
≥
−
⇒
|
x
|
≥
1
⇒
−
1
≤
x
≤
1
∴
x
∈
[
−
1
,
−
1
+
√
5
2
)
Suggest Corrections
0
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