Question
Download Solution PDFIf x = 222, y = 223 and z = 224, then find the value of x3 + y3 + z3 - 3xyz.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
x = 222,
y = 223
z = 224
Formula used:
x3 + y3 + z3 - 3xyz = (1/2)(x + y + z)[(x - y)2 + (y - z)2 + (z - x)2]
Calculation:
x3 + y3 + z3 - 3xyz = (1/2)(222 + 223 + 224)[(222 - 223)2 + (223 - 224)2 + (224 - 222)2]
⇒ x3 + y3 + z3 - 3xyz = (1/2)(669)[(1) + (1) + (4)]
⇒ x3 + y3 + z3 - 3xyz = 3 × 669
⇒ x3 + y3 + z3 - 3xyz = 2007
∴ The value of x3 + y3 + z3 - 3xyz is 2007.
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.