If, \(\frac{r}{13} + \frac{13}{r} = 1\) then the value of r3 is:

This question was previously asked in
SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 3)
View all SSC CGL Papers >
  1. -2157
  2. 2197
  3. 2157
  4. -2197

Answer (Detailed Solution Below)

Option 4 : -2197
super-pass-live
Free
SSC CGL Tier 1 2025 Full Test - 01
3.5 Lakh Users
100 Questions 200 Marks 60 Mins

Detailed Solution

Download Solution PDF

Given:

\(\frac{r}{13} + \frac{13}{r} = 1\)

Concept used:

If x + (1/x) = 1

then x3 = - 1

Calculation:

Let (r/13) = x

According to the question:

⇒ \(\frac{r}{13} + \frac{13}{r} = 1\)

⇒ x + 1/x = 1

then x3 = - 1

Now, putting the value of x

⇒ (r/13)3 = - 1

⇒ r3 = - 2197

∴ The correct answer is -2197.

Additional InformationGiven - x + 1/x = 1

Formula Used - a3 + b3 = (a + b)(a2 – ab + b2)

Calculation:

x + 1/x = 1

⇒ x2 + 1 = x

⇒ x2 - x + 1 = 0      ---(1)

Multiply (x + 1) into both side of eq (1)

⇒ (x + 1)( x2 – x + 1) = 0

⇒ x3 + 1 = 0

⇒ x3 = -1

Latest SSC CGL Updates

Last updated on Jul 19, 2025

-> The SSC CGL Notification 2025 has been announced for 14,582 vacancies of various Group B and C posts across central government departments.

-> CSIR NET City Intimation Slip 2025 has been released @csirnet.nta.ac.in. 

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

->  Aspirants should visit the official website @ssc.gov.in 2025 regularly for CGL Exam updates and latest announcements.

-> Candidates had filled out the SSC CGL Application Form from 9 June to 5 July, 2025. Now, 20 lakh+ candidates will be writing the SSC CGL 2025 Exam on the scheduled exam date. Download SSC Calendar 2025-25!

-> In the SSC CGL 2025 Notification, vacancies for two new posts, namely, "Section Head" and "Office Superintendent" have been announced.

-> 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, with the age limit varying from post to post. 

-> The SSC CGL Salary structure varies by post, with entry-level posts starting at Pay Level-4 (Rs. 25,500 to 81,100/-) and going up to Pay Level-7 (Rs. 44,900 to 1,42,400/-).

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

More Algebra Questions

Get Free Access Now
Hot Links: teen patti bindaas teen patti royal - 3 patti teen patti all app teen patti game paisa wala