SSC CGL 26 Oct 2014 Shift 2 Paper

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Question : 116 of 200

Marks: +1, -0

If

x^2

– 3x + 1 = 0, then the value of

{x^6+x^4+x^2+1}/x^3

will be

18
15
21
30

Solution:

x^2

– 3 x + 1 = 0
⇒

x^2

+1 = 3 x
⇒

{x^2+1}/x

= 3
⇒ x +

1/x

= 3 ... (i)
∴

{x^6+x^4+x^2+1}/x^3

=

x^6/x^3 + x^4/x^3

+

x^2/x^3 + 1/x^3

=

x^3

+ x +

1/x + 1/x^3

=

(x^3+1/x^3)

+

(x+1/x)

=

(x+1/x)^3

- 3 . x .

1/x (x+1/x)

+

(x+1/x)

=

3^3

– 3 × 3 + 3 = 27 – 9 + 3
= 21

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