SSC CGL 16 Aug 2015 Shift 1 Paper

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Question : 130 of 200

Marks: +1, -0

If

{x^{24}+1}/x^{12}

= 7 then the value of

{x^{72}+1}/x^{36}

is

433
322
343
432

Solution:

⇒

x^{24}/x^{12} + 1/x^{12}

= 7
⇒

x^{12}+1/x^{12}

= 7
∴

{x^{72}+1}/x^{36}

=

x^{72}/x^{36} + 1/x^{36}

=

x^{36}+1/x^{36}

=

(x^{12}+1/x^{12})^3

- 3 ×

x^{12}

×

1/x^{12} (x^{12}+1/x^{12})

[Since

a^3+b^3

=

(a+b)^3

- 3 ab (a+b)]
=

7^3

- 3 × 7 = 343 - 21 = 322

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