Discussion
Let λ be the A.M. between α and β and also G.M. between α and β . Then α2 + β2 =
Answer: E
\(\alpha^{2} + \beta^{2}\) equals \(2\alpha\beta\).
If \(\lambda\) is both the A.M. and the G.M. of \(\alpha\) and \(\beta\), then
\[ \begin{aligned} \frac{\alpha + \beta}{2} &= \sqrt{\alpha\beta} \\ (\alpha + \beta)^{2} &= 4\alpha\beta \\ \alpha^{2} + \beta^{2} &= 4\alpha\beta - 2\alpha\beta = 2\alpha\beta \end{aligned} \]
(In fact this forces \((\alpha - \beta)^{2} = 0\), so \(\alpha = \beta\).) \(4\alpha\beta\) is \((\alpha + \beta)^{2}\), not \(\alpha^{2} + \beta^{2}\); the other multiples do not follow.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development