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SSC CGL 2022 PYQ — Question 62

SSC CGL - 20 April 2022 - Shift 2 • Quantitative Aptitude • Q62

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If x\sqrt{x}-1x\frac{1}{\sqrt{x}}= 5\sqrt{5}, x ≠ 0, then what is the value of 

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 46

 ⇒ Diving numerator and denominator by x, we 

(x3 + 1/x3)/(x + 1/x)

  x\sqrt{x}-1x\frac{1}{\sqrt{x}}= 5\sqrt{5}  

Squaring both sides, we get

x + 1/x - 2 = 5 ⇒ x + 1/x = 7

Cubing both the sides

⇒ [x + 1/x]3 = 73

⇒ x3 + 1/x3 + 3 × 7 = 343

⇒ x3 + 1/x3 = 343 - 21 = 322

(x3 + 1/x3)/(x + 1/x) = 322/7 = 46