If \({\rm x} + \frac{1}{{\rm x}} = - 14 \), and x < -1, what will be the value of \({{\rm x}^2} - \frac{1}{{{{\rm x}^2}}}\) ?

This question was previously asked in
SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 1)
View all SSC CGL Papers >
  1. - 112√3  
  2. 112√3  
  3. -140√2  
  4. 140√2  

Answer (Detailed Solution Below)

Option 2 : 112√3  
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

Given:

\({\rm x} + \frac{1}{{\rm x}} = - 14\)

Concept used:

(a2 - b2) = (a + b)(a - b)

Calculation:

\({\rm x} + \frac{1}{{\rm x}} = - 14 \)

⇒ \({\rm x^2} + \frac{1}{{\rm x^2}} +2= 196 \)

⇒ \({\rm x^2} + \frac{1}{{\rm x^2}} +2-4= 196-4 \)

⇒ \({\rm x^2} + \frac{1}{{\rm x^2}} -2= 192 \)

⇒ \(({\rm x} - \frac{1}{{\rm x}})^2= 192 \)

⇒ \({\rm x} - \frac{1}{{\rm x}} =\pm 8√3 \)

As x < -1 So, \({\rm x} - \frac{1}{{\rm x}} =- 8\sqrt3 \)

Now,

\({{\rm x}^2} - \frac{1}{{{{\rm x}^2}}}\) = (- 14) × (\(-8\sqrt 3 \))

⇒ \(112\sqrt 3 \)

∴ The required answer is \(112\sqrt 3 \).

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 rules teen patti game online teen patti master downloadable content teen patti tiger teen patti live