SSC CGL 4 Sep 2016 Paper

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Question : 66 of 100

Marks: +1, -0

If 2x +

2/x

= 3 , then the value of

x^3+1/x^3

+ 2 is

$3/4$
$4/5$
$5/8$
$7/8$

Solution:

2x +

2/x

= 3
On dividing by 2,
x +

1/x

=

3/2

On cubing both sides,

(x+1/x)^3

=

(3/2)^3

⇒

x^3+1/x^3

+ 3

(x+1/x)

=

{27}/8

⇒

x^3+1/x^3

+ 3 ×

3/2

=

{27}/8

⇒

x^3+1/x^3

+

9/2

=

{27}/8

⇒

x^3+1/x^3

=

{27}/8 - 9/2

=

{27 - 36}/8

=

9/8

∴

x^3+1/x^3

+ 2
= 2 -

9/8

=

{16-9}/8

=

7/8

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