If x + 1 /x = \sqrt3 then the value of x^18 + x^12 + x^6 + 1 is

RRB NTPC Mains or Stage 2 Model Paper 9 with solutions

Question : 39 of 120

Marks: +1, -0

x + 1 /x = √3

then the value of

x^18 + x^12 + x^6 + 1

Solution:

(a)

x +1/x =√ 3

Cubing both sides,

x^3 +1/X^3[X+1/X]= ( √3)^3

⇒ x^3 +1/{X^ 3}+ 3√ 3= 3 √3⇒x^3+1/{x^3}=0

Now,

x^18 + x^12 + x^6 + 1

= x^12 (x^6 + 1) + 1(x^6 + 1) = (x^12 + 1) (x^6 + 1)

= (x^12 + 1) . x^3[x^ 3+1/{x^3}]=0

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