If x/{x^2 x \times5x + 1} =1/6 , then what is the value of x^3 + 1 /x^3 ?

SSC CPO SI and ASI Model Paper 2

Question : 102 of 200

Marks: +1, -0

If $x/{x^2 x ×5x + 1} =1/6$ , then what is the value of $x^3 + 1 /x^3 ?$

Solution:

(1)

6x = x^2 –5x +1

x^2–11x +1 = 0

⇒

x –11 + 1/X = 0

⇒x + 1 /X=11

By cubing both sides:

x ^3+ 1/X^3 +3 × 1/x [x + 1/x] =1331

⇒x ^3+ 1/x^3 +33 =1331

⇒x^3 + 1 /x^3=1298

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