Question
Download Solution PDFयदि x2 - 7x + 1 = 0, और 0 < x < 1, x2 - \(\frac{1}{x^2}\) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFप्रयुक्त सूत्र:
x + (1/x) = a
तब x - (1/x) = √(a2 - 4)
गणना:
⇒ x2 - 7x + 1 = 0
x से विभाजित करने पर हमें प्राप्त होता है:
⇒ x - 7 + (1/x) = 0
⇒ x + (1/x) = 7
अब, x - (1/x) = -√(49 - 4) = -√45 = -3√5
[यहाँ 0 < x < 1 अत: x - 1/x < 0]
⇒ x2 - (1/x2) = (x - 1/x)(x + 1/x)
⇒ 7 × (-3√5)
⇒ -21√5
∴ सही उत्तर - 21√5 है।
Mistake Points
यहाँ 0 < x < 1
⇒ 1/x > 1
⇒ x - 1/x < 0
इसलिए, x2 - 1/x2 = [x - (1/x)] [x + (1/x)] < 0
Last updated on Jul 10, 2025
-> The SSC CGL Application Correction Window Link Live till 11th July. Get the corrections done in your SSC CGL Application Form using the Direct Link.
-> 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.