Check sibling questions

Misc 13 - If (a + bx)/(a - bx) = (b + cx)/(b-cx) = (c + dx) - Miscellaneous

Misc 13 - Chapter 9 Class 11 Sequences and Series - Part 2
Misc 13 - Chapter 9 Class 11 Sequences and Series - Part 3

This video is only available for Teachoo black users

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Misc 13 If , (a+bx)/(aβˆ’bx) = (b+cx)/(bβˆ’cx) = (c+dx)/(aβˆ’dx) (x β‰  0)then show that a, b, c and d are in G.P. Introduction Componendo dividendo If π‘₯/𝑦 = π‘Ž/𝑏 Applying componendo dividendo (π‘₯ + 𝑦)/(π‘₯ βˆ’ 𝑦) = (π‘Ž + 𝑏)/(π‘Ž βˆ’ 𝑏) Eg: Taking 1/2 = 4/8 (1+ 2)/(1 βˆ’ 2) = (4 + 8)/(4 βˆ’ 8) 3/(βˆ’1) = 12/(βˆ’4) -3 = -3 Misc 13 If , (a+bx)/(aβˆ’bx) = (b+cx)/(bβˆ’cx) = (c+dx)/(aβˆ’dx) (x β‰  0)then show that a, b, c and d are in G.P. We have (a+bx)/(aβˆ’bx) = (b+cx)/(bβˆ’cx) = (c+dx)/(c βˆ’ dx) & we want to show that a, b, c, d are in G.P. Taking (a+bx)/(aβˆ’bx) = (b+cx)/(bβˆ’cx) = (c+dx)/(c βˆ’ dx) Applying componendo dividendo (a + bx + a βˆ’ bx)/((a + bx) βˆ’(aβˆ’bx)) = (b + cx + (b βˆ’ cx))/(b + cx βˆ’(b βˆ’ cx)) = (c + dx + (c βˆ’ dx))/(c + dx βˆ’ (c βˆ’ dx)) (a + a + bx βˆ’ bx)/(𝑏π‘₯+ bx βˆ’ a + a ) = (b + b + cx βˆ’ cx)/(cx + cx βˆ’ 𝑏 + 𝑏) = (c + dx + c βˆ’ dx)/(dx + dx βˆ’ 𝑐 + 𝑐) (2π‘Ž+0)/(2𝑏π‘₯+0) = (2𝑏 + 0)/(2𝑐π‘₯ + 0) = (2𝑐+0)/(2𝑑π‘₯+0) 2π‘Ž/2𝑏π‘₯ = 2𝑏/2𝑐π‘₯ = 2𝑐/2𝑑π‘₯ π‘Ž/𝑏π‘₯ = 𝑏/𝑐π‘₯ = 𝑐/𝑑π‘₯ a/b " =" b/c = c/d b/a " =" c/b = d/c Thus, a, b, c & d are in GP because their common ratio is same

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.