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SSC Selection Post 2022 PYQ — Question 55

SSC Selection Post - Graduation Level 2022 - 10 Feb 2022 - Shift 3 • Quantitative Aptitude • Q55

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If x2 - 4x - 3 = 0, then what is the value of (x4−27x2)(x2+4x−3)(x^4-{27\over{x^2}})\over(x^2+4x-3)?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 12121\over2.

x2 - 4x - 3 = 0

⇒ x - 3/x = 4

⇒ (x - 3/x)3 = 43

⇒ x3 - 27/x3 - 3(x)(3/x)(x - 3/x) = 64

⇒ x3 - 27/x3 = 100

Now, (x4 - 27/x2)/(x2 + 4x - 3)

= (x3 - 27/x3)/(x + 4 - 3/x)

= 100/(4 + 4)

= 121212\frac{1}{2}