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SSC CHSL 2023 PYQ — Question 67

SSC CHSL - 07 Aug 2023 - Shift 2 • Quantitative Aptitude • Q67

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If (x + 1x\frac{1}{x}) = 5, then the value of (x5 + 1x5\frac{1}{x^5}) is:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 2525.

If x + (1/x) = a then x2 + 1/x2 = a2 - 2 and x3 + 1/x3 = a3 - 3a

Here, x + (1/x) = 5

So, x2 + 1/x2 = 52 - 2 = 25 - 2 = 23

Also, x3 + 1/x3 = 53 - 3a = 125 - 15 = 110

Now, 

x5 + 1/x5 = (x2 + 1/x2)(x3 + 1/x3) - (x + 1/x)

= (23 × 110) - 5

= 2530 - 5 = 2525

Therefore, the value of the given expression is 2525.