Question
Download Solution PDFIf \(y + {{1} \over y} = 3\), then what is the value of \({{1} \over y^3} + y^3 + 2 \)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(y + {{1} \over y} = 3\)
Concept used:
(a + b)3 = a3 + b3 + 3ab(a + b)
Calculation:
\(y + {{1} \over y} = 3\)
⇒ \((y + {{1} \over y})^3 = 27\)
⇒ \(y^3 + {{1} \over y}^3 +3(y +\frac{1}{y})= 27\)
⇒ \(y^3 + {{1} \over y}^3 +3 \times 3= 27\)
⇒ \(y^3 + {{1} \over y}^3 +9= 27\)
⇒ \(y^3 + {{1} \over y}^3= 18\)
⇒ \({{1} \over y^3} + y^3 + 2 \) = 20
∴ The required answer is 20.
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.