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SSC CHSL 2023 PYQ — Question 52

SSC CHSL - 09 Aug 2023 - Shift 1 • Quantitative Aptitude • Q52

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If x = (6\sqrt6 - 1)1/3, then the value of (x−1x)3(x - \frac 1 x)^3 + 3(x−1x)(x - \frac 1 x) is:

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 46−65\frac{4\sqrt{6} - 6}{5}.

x = (√6 - 1)1/3 

⇒ x3 = (√6 - 1)

Also, 1/x = (√6 - 1)(-1/3) 

⇒ 1/x3 = 1/(√6 - 1) = (√6 + 1)/5

Now, (x - 1/x)3 = x3 - 1/x3 - 3(x - 1/x)

⇒ (x - 1/x)3 + 3(x - 1/x) = x3 - 1/x3

= (√6 - 1) - (√6 + 1)/5

= (4√6 - 6)/5

Therefore, the required value is (4√6 - 6)/5.