Question
Download Solution PDFIf y = 1 + √3 + √4, then the value of 2y4 - 8y3 - 6y2 + 28y - 84 is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
y = 1 + √3 + √4
Formula used:
(x + y)2 = x2 + y2 +2xy
Calculations:
⇒ y = 1 + √3 + √4,
⇒ y = 1 + √3 + 2 = 3 + √3
⇒ y2 = (3 + √3)2
⇒ y2 = 9 +3 + 6√3 = 12 + 6√3
According to the question,
⇒ 2y4 - 8y3 - 6y2 + 28y - 84
⇒ 2y2(y2 - 4y - 3) + 28(3 + √3) - 84
⇒ 2y2(y2 - 4y - 3 + 4 - 4) + 84 + 28√3 - 84
⇒ 2y2(y2 - 4y + 4 - 7) + 28√3
⇒ 2y2{(y-2)2 - 7} + 28√3
Now put the value of y and y2
⇒ 2(12 + 6√3){(3 + √3 -2)2 - 7} + 28√3
⇒ (24 + 12√3){(1 + √3)2 - 7} + 28√3
⇒ (24 + 12√3){1 + 3 + 2√3 - 7} + 28√3
⇒ (24 + 12√3){2√3 - 3} + 28√3
⇒ 48√3 - 72 + 72 - 36√3 + 28√3
⇒ 40√3
⇒ Hence, Option 1 is correct
Last updated on Jun 13, 2025
-> The SSC CGL Notification 2025 has been released on 9th June 2025 on the official website 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 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.
-> Candidates should also use the SSC CGL previous year papers for a good revision.