If x + [1 /x ] = p, then what is x^6 +[1/X^ 6] equal to?

Correct Answer is : p6–6p4+9p2–2

RRB NTPC Mains or Stage 2 Model Paper 5 with solutions

Question : 16 of 120

Marks: +1, -0

x + [1 /x ] = p

, then what is

x^6 +[1/X^ 6]

equal to?

Solution:

(d) Given,

x +1/x= p

⇒[x+1 /x]^2= p2

⇒ x^2 +1/{x^ 2}+2= p^2

⇒ x^2 +1/{x^ 2}+2= p^2-2

⇒[x^2+1/{x^2}]^3= (p^2 – 2)^3

⇒ x^6 +1/{x^6}+3 [x^2 +1/x ^2]=(p^2-2)^3

⇒x^6 +1/x^6+3[x^2+1/{x^2}]=p^6- 8 – 6p^2 (p^2 – 2)

⇒ x^6 + 1/{x^6}+ 3(p^2 – 2) = p^6 – 8 – 6p^4 + 12p^2

[from equation (i)]

= x^6 +1/{x^ 6}=p^6-6p^4 + 9p^2 – 2

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