SSC CHSL 20 Dec 2015 Shift 2 Paper

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Question : 103 of 200

Marks: +1, -0

If

(a +1/ a ) ^2= 3

, then find the value of

a^ 30 + a ^24 + a^ 18

+ a^ 12 + a ^6 + 1

-1
1
27
0

Solution:

Given :

(a +1/ a ) ^2= 3

⇒

(a +1/ a ) = √3

------(i)
Cubing both sides, we get :
⇒

(a +1/ a ) ^3= (√3)^3

⇒

a^3 +1/ a ^3

+ 3(a)( 1/a )(a + 1/ a ) = 3 √3

⇒

a ^3 + 1/a ^3 + 3 √3 = 3 √3

⇒

a^3 + 1/a ^3 = 0

⇒

{a^6 +1}/a^3=0

⇒

a^6 = −1

To find :

a ^30 + a^ 24 + a ^18

+ a^ 12 + a ^6 + 1

=

(a ^6) ^5 + (a ^6) ^4 + (a^ 6) ^3

+ (a ^6)^ 2 + (a^ 6) + 1

=

(−1) ^5 + (−1) ^4 + (−1) ^3

+ (−1)^ 2 + (−1) + 1

=

−1 + 1 − 1 + 1 − 1 + 1 = 0

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