If x + 1 /x =\sqrt 3 , then the value of x^18 + x^12 + x^6 + 1 is

RRB NTPC Mains or Stage 2 Model Paper 4 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}+3[x+1/x]=(√3)^3

3√ 3 = 3√ 3

⇒ x^3 +1/{x^ 3} = 0

Now,

x^18 + x^12 + y^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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