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Byju's Answer
Standard XII
Mathematics
Methods of Solving a Quadratic Equation
The inequalit...
Question
The inequality
|
x
|
2
−
|
x
|
−
2
2
|
x
|
−
|
x
|
2
−
2
>
0
holds if and only if
A
−
1
<
x
<
−
−
2
3
or
2
3
<
x
<
1
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B
none of these
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C
2
3
<
x
<
1
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D
−
2
<
x
<
2
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Solution
The correct option is
D
−
2
<
x
<
2
Let
|
x
|
=
t
⇒
t
2
−
t
−
2
2
t
−
t
2
−
2
>
0
⇒
(
t
−
2
)
(
t
+
1
)
t
2
−
2
t
+
2
<
0
⇒
(
t
−
2
)
(
t
+
1
)
(
(
t
−
1
)
2
+
1
)
<
0
Here
(
t
−
1
)
2
+
1
>
0
∀
t
∈
R
⇒
(
t
−
2
)
(
t
+
1
)
<
0
⇒
−
1
<
t
<
2
⇒
−
1
<
|
x
|
<
2
⇒
−
2
<
x
<
2
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0
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