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SSC CGL 2022 PYQ — Question 74

SSC CGL - 18 April 2022 - Shift 3 • Quantitative Aptitude • Q74

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If √x - 1/√x = √3, then what is the value of x4 + 1x4\frac{1}{x^4}?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 527

Formula used:

(a - b)2 = a2 + b2 - 2ab      ---- (1)

(a + b)2 = a2 + b2 + 2ab       ---- (2)

Calculations:

⇒ (√x - 1/√x)2 = x + 1/x - 2

⇒ 3 + 2 = x + 1/x       ---- (3)

Using equation (2) in (3)

⇒ (x + 1/x)2 = x2 + 1/x2 + 2

⇒ 25 - 2 = x2 + 1/x2

Now,

⇒ (x2 + 1/x2)2 = x4 + 1/x4 + 2

⇒ 529 - 2 = x4 + 1/x4

⇒ x4 + 1/x4 = 527