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Standard XII
Mathematics
Question
If
2
(
x
2
+
1
)
=
5
x
, find
x
3
−
1
x
3
.
±
17
3
±
63
8
±
13
8
±
3
8
A
±
17
3
B
±
13
8
C
±
63
8
D
±
3
8
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Solution
Verified by Toppr
2
(
x
2
+
1
)
=
5
x
=
>
x
2
+
1
x
=
5
2
=
>
x
+
1
x
=
5
2
Squaring both sides,
=
>
x
2
+
1
x
2
+
2
(
x
)
+
(
1
x
)
=
25
4
=
>
x
2
+
1
x
2
=
25
4
−
2
=
>
x
2
+
1
x
2
=
17
4
Now,
(
x
−
1
x
2
)
2
=
x
2
+
1
x
2
−
2
(
x
)
+
(
1
x
)
=
17
4
−
2
=
9
4
=
>
x
−
1
x
=
±
√
9
4
=
±
3
2
Now,
x
3
−
1
x
3
=
(
x
−
1
x
)
[
(
x
2
+
1
x
2
+
(
x
)
(
1
x
)
]
=
(
±
3
2
)
(
17
4
+
1
)
=
(
±
3
2
)
(
21
4
)
=
±
63
8
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