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SSC CGL 2022 PYQ — Question 56

SSC CGL - 05 Dec 2022 - Shift 1 • Quantitative Aptitude • Q56

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If x + (1/x) = -14, and x < -1, what is the value of x2 - (1/x2)?

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Correct answer: B

Explanation

The correct answer is Option 2 i.e. 112 √3 

Formula used:

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

Calculations:

⇒ x + 1/x = -14

Squaring both sides, we get

⇒ x2 + 1/x2 + 2 = 196

⇒ x2 + 1/x2 = 194

Now, (x - 1/x)2 = x2 + 1/x2 - 2 = 192

⇒ (x - 1/x) = - 8√3 as x < -1

Using equation (1), we get

⇒ x2 - 1/x2 = (-14)(-8√3) = 112√3