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  1. If   2x +
    1
    = 3, then the value of   x3 +
    1
    + 2 is
    xx3
    1. 3
      4
    2. 4
      5
    3. 5
      8
    4. 7
      8
Correct Option: D

2x +
2
= 3
x

On dividing by 2,
x +
1
=
3
x2

On cubing both sides,
x +
1
3 =
3
3
x2

⇒  x3 +
1
+ 3x +
1
=
27
x3x8

⇒  x3 +
1
+ 3 ×
3
=
27
x328

⇒  x3 +
1
+
9
=
27
x328

⇒  x3 +
1
=
27
9
x382

=
27 − 26
=
9
88

∴  x3 +
1
+ 2
x3

= 2 −
9
=
16 − 9
88

=
7
8



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