Question
Download Solution PDFIf x + \(\frac{1}{x}\) = 1, then the value of x12 + x9 + x6 + x3 + 1 is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The value of x12 + x9 + x6 + x3 + 1
if x + (1/x) = 1
x2 + 1 = x
x2 - x + 1 = 0
(x + 1)(x2 - x + 1) = 0 (x + 1)
(x3 + 13) = 0
x3 = -1
Formula used:
x + 1/x = 1 then x3 = -1
Calculation:
According to the question,
x12 + x9 + x6 + x3 + 1
⇒ (x3)4 + (x3)3 + (x3)2 + (x3) + 1
⇒ (−1)4 + (-1)3 + (-1)2 + (-1) + 1
⇒ 1 - 1 + 1 - 1 + 1
⇒ 3 - 2 = 1
∴ The value of x12 + x9 + x6 + x3 + 1 is 1.
Last updated on Jun 9, 2025
-> The SSC CGL Notification 2025 has been released on 9th June 2025 at ssc.gov.in.
-> The SSC CGL exam registration process is now open and will continue till 4th July 2025, so candidates must fill out the SSC CGL Application Form 2025 before the deadline.
-> 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 SSC CGL exam form.
-> Candidates can refer to the SSC CGL syllabus for a better understanding of the exam structure and pattern.
-> The SSC 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.
-> Candidates should also use the SSC CGL previous year papers for a good revision.