SSC CGL 26 Oct 2014 Shift 1 Paper

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Question : 114 of 200

Marks: +1, -0

If

x^4+1/x^4

= 119, then the value of

x^3-1/x^3

is

± 33
36
- 36
± 36

Solution:

x^4+1/x^4

= 119
⇒

(x^2+1/x^2)^2

- 2 = 119
⇒

(x^2+1/x^2)^2

= 119 + 2 = 121
⇒

(x^2+1/x^2)^2

=

11^2

⇒

x^2+1/x^2

= 11
⇒

(x-1/x)^2

+ 2 = 11
⇒

(x-1/x)^2

= 11 - 2 = 9
⇒

(x-1/x)^2

=

3^2

⇒

x-1/x

= 3
On cubing both sides,

x^3-1/x^3 - 3(x-1/x)

=

3^3

⇒

x^3-1/x^3

- 3 × 3 = 27
⇒

x^3-1/x^3

= 27 + 9 = 36

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