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SSC CGL 2023 PYQ — Question 54

SSC CGL - 26 Jul 2023 - Shift 1 • Quantitative Aptitude • Q54

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If x2 - 8x - 1 = 0, what is the value of x2+1x2?x^2 + \frac{1}{x^2}?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 66.

Given that, x2 - 8x - 1 = 0

Dividing the given equation by x,

⇒ x−8−1x=0x - 8 - {1 \over x} = 0

⇒ x−1x=8x - {1 \over x} = 8

Now squarying both sides of the equation,

⇒ (x−1x)2=82(x - {1 \over x})^2 = 8^2

⇒ x2+1x2−2x^2 + {1\over x^2} - 2  = 64

⇒ x2+1x2x^2 + {1\over x^2}  = 66

Hence the value of x2+1x2x^2 + {1\over x^2}  is 66.