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SSC CGL 2023 PYQ — Question 64

SSC CGL - 19 July 2023 - Shift 3 • Quantitative Aptitude • Q64

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If x2 - 7x + 1 = 0, and 0 < x < 1, what is the value of x2 −1x2-\frac{1}{x^2}?
 

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Correct answer: B

Explanation

The correct answer is option 2 i.e. −215-21\sqrt5.

Given that

If x2 - 7x + 1 = 0, and 0 < x < 1,

Calculation

x + 1/x = 7

Squaring both sides

⇒ x2 + 1/x2 = 49 - 2 = 47

⇒ (x - 1/x)2 + 2 = 47

⇒ (x - 1/x)2 = 47 - 2 = 45

⇒ x - 1/x = ±3√5 

we take only negative value (0 < x < 1) so, x - 1/x = - 3√5 

Hence,   x2 −1x2-\frac{1}{x^2} = (x + 1/x)(x - 1/x) = 7 × - 3√5 = - 21√5