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Mathematics
The equation |x| + | (x/x-1)|= (x2/|x-1|) will be always true for x , belonging to
Q. The equation |x| +
∣
x
−
1
x
∣
=
∣
x
−
1∣
x
2
will be always true for
x
, belonging to
1665
218
AMU
AMU 2018
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A
[
0
,
1
)
B
{
0
}
∪
(
1
,
∞
)
C
(
−
1
,
1
)
D
(
−
∞
,
∞
)
Solution:
We have,
∣
x
∣
+
∣
∣
x
−
1
x
∣
∣
=
∣
x
−
1∣
x
2
We know that,
∣
a
∣
+
∣
b
∣
=
∣
a
+
b
∣
. Then,
ab
≥
0
Here,
∣
x
∣
+
∣
∣
x
−
1
x
∣
∣
=
∣
∣
x
+
x
−
1
x
∣
∣
∣
x
∣
+
∣
∣
x
−
1
x
∣
∣
=
∣
∣
x
−
1
x
2
∣
∣
=
∣
x
−
1∣
x
2
∴
x
⋅
x
−
1
x
≥
0
⇒
x
−
1
x
2
≥
0
⇒
x
∈
{
0
}
∪
(
1
,
∞
)