Question
Download Solution PDFयदि x + \(\frac{1}{2x}\) = 3 है, तो 8x3 + \(\rm \frac{1}{x^3}\) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया:
x + \(\frac{1}{2x}\) = 3
प्रयुक्त अवधारणा:
सरल गणनाओं का प्रयोग किया जाता है
गणना:
⇒ x + \(\frac{1}{2x}\) = 3
दोनों पक्षों में 2 का गुणा करने पर, हमें प्राप्त होता है
⇒ 2x + \(\frac{1}{x}\) = 6 .................(1)
अब, दोनों पक्षों को घन करने पर,
⇒ \((2x + \frac{1}{x})^3 = 6^3\)
⇒ \(8x^3 + \frac{1}{x^3} + 3(4x^2)(\frac{1}{x})+3(2x)(\frac{1}{x^2})=216\)
⇒ \(8x^3 + \frac{1}{x^3} + 12x+\frac{6}{x}=216\)
⇒ \(8x^3 + \frac{1}{x^3}= 216 - 6(2x+\frac{1}{x})\)
⇒ \(8x^3 + \frac{1}{x^3}= 216- 6(6)\) ..............(1) से
⇒ \(8x^3 + \frac{1}{x^3}= 216- 36\)
⇒ \(8x^3 + \frac{1}{x^3}= 180\)
⇒ इसलिए, उपरोक्त समीकरण का मान 180 है।
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.