If x4 - 6x2 – 1 = 0, then the value of x6 - 5x2 + 5/x2 - 1/x6 + 5 is:
Show answer & explanation
Correct answer: D
Explanation
Correct Answer is option 4 i.e. 209
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Concept |
Application |
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(a – 1/a)3 = a3 – 1/a3 – 3 × 1 × (a – 1/a) |
x4 – 6x2 – 1 = 0 ⇒ x4– 1 = 6x2 ⇒ x2 – 1/x2 = 6 Taking cube both the sides: ⇒ x6 – 1/x6 – 3 (x2 – 1/x2) = 63 ⇒ x6 – 1/x6 – 3 × 6 = 216 ⇒ x6 – 1/x6 = 234 Hence, x6 – 5x2 + 5/x2 – 1/x6 + 5 ⇒ (x6 – 1/x6) – 5(x2 – 1/x2) + 5 ⇒ 234 – 5 × 6 + 5 ⇒ 209 |