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SSC CHSL 2019 PYQ — Question 68

SSC CHSL - 3rd July 2019 - Shift 1 • Quantitative Aptitude • Q68

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If x is real, and x4 – 5x2 – 1 = 0, then the value of x6 – 3x2 + 3/x2 – 1/x6 + 1 is:

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Correct answer: D

Explanation

Correct Answer is option 4 i.e. 126

Concept

Application

(a – b)3 = a3 – b3 – 3ab (a – b)

x4 – 5x2 – 1 = 0

⇒ x4 – 1 = 5x2

⇒ x2 – 1/x2 = 5

Taking cube both sides:

⇒ x6 – 1/x6 – 3(x2 – 1/x2) = 125

⇒ x6 – 1/x6 – 3 × 5 = 125

⇒ x6 – 1/x6 = 125 + 15 = 140

Now,

x6 – 3x2 + 3/x2 – 1/x6 + 1

⇒ x6 – 1/x6 – 3 (x2 – 1/x2) + 1

⇒ 140 – 3 × 5 + 1

⇒ 126