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SSC CGL 2024 PYQ — Question 59

SSC CGL - 26 Sep 2024 - Shift 3 • Quantitative Aptitude • Q59

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If xx2−2x+1=13{x\over {x^2-2x+1}}={1\over3},then the value of x3+1x3x^3+{1\over x^3} is:

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 110.

(a + b)3 = a3 + b3 + 3ab(a + b)

Now, x/(x2 - 2x + 1) = 1/3

⇒ x/(x - 1)2 = 1/3

⇒ 3x = (x - 1)2

⇒ 3x = x2 - 2x + 1

⇒ x2 - 5x + 1 = 0

⇒ x - 5 + (1/x) = 0   [Dividing both sides by x]

⇒ x + (1/x) = 5   .....(1)

⇒ [x + (1/x)]3 = 53   [Taking cube of both sides]

⇒ x3 + (1/x3) + 3[x + (1/x)] = 125

⇒ x3 + (1/x3) + 15 = 125   [∵ x + (1/x) = 5]

⇒ x3 + (1/x3) = 125 - 15 = 110

Therefore, the value of the given expression is 110.