यदि \((x - \frac{1}{x})\) = √6, और x > 1 है, तो \((x^8 - \frac{1}{x^8})\) का मान कितना है?

This question was previously asked in
SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 2)
View all SSC CGL Papers >
  1. 1024√15
  2. 992√15
  3. 998√15
  4. 1012√15

Answer (Detailed Solution Below)

Option 2 : 992√15
super-pass-live
Free
SSC CGL Tier 1 2025 Full Test - 01
3.3 Lakh Users
100 Questions 200 Marks 60 Mins

Detailed Solution

Download Solution PDF

दिया गया है:

x - (1/x) = √6

प्रयुक्त सूत्र:

x8 - (1/x8) = {x4 + (1/x4)} × {x2 + (1/x2)} × {x + (1/x)} × {x - (1/x)}

यदि x - (1/x) = a है, तब x + (1/x) = √(a2 + 4)

गणना:

x - (1/x) = √6

x2 + (1/x2) = (√6)2 + 2 = 8

दोनों पक्षों का वर्ग करने पर:

x4 + (1/x4) = (8)2 - 2 = 62

यदि x - (1/x) = a है, तब x + (1/x) = √{(√a)2 + 4}, इस सूत्र का उपयोग करने पर,

x + (1/x) = √{(√6)2 + 4} = √10

मानों को प्रतिस्थापित करने पर, हमें प्राप्त होता है:

x8 - (1/x8) = {x4 + (1/x4)} × {x2 + (1/x2)} × {x + (1/x)} × {x - (1/x)}

⇒ 62 × 8 × √10 × √6 = 496 × 2 × √15 = 992√15

∴ सही उत्तर 992√15 है।

Latest SSC CGL Updates

Last updated on Jul 9, 2025

-> The SSC CGL Notification 2025 for the Combined Graduate Level Examination has been officially released on the SSC's new portal – www.ssc.gov.in.

-> Bihar Police Admit Card 2025 Out at csbc.bihar.gov.in

-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.

-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.

->  Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.

-> Candidates can refer to the CGL syllabus for a better understanding of the exam structure and pattern.

-> The CGL Eligibility is a bachelor’s degree in any discipline.

-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.

-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.

-> The AP DSC Answer Key 2025 has been released on its official website.

-> The UP ECCE Educator 2025 Notification has been released for 8800 Posts.

More Algebra Questions

Get Free Access Now
Hot Links: teen patti real money app teen patti apk download teen patti master new version