Last updated at May 29, 2018 by Teachoo

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Misc 13 If , (a+bx)/(aโbx) = (b+cx)/(bโcx) = (c+dx)/(aโdx) (x โ 0)then show that a, b, c and d are in G.P. Introduction Componendo dividendo If ๐ฅ/๐ฆ = ๐/๐ Applying componendo dividendo (๐ฅ + ๐ฆ)/(๐ฅ โ ๐ฆ) = (๐ + ๐)/(๐ โ ๐) Eg: Taking 1/2 = 4/8 (1+ 2)/(1 โ 2) = (4 + 8)/(4 โ 8) 3/(โ1) = 12/(โ4) -3 = -3 Misc 13 If , (a+bx)/(aโbx) = (b+cx)/(bโcx) = (c+dx)/(aโdx) (x โ 0)then show that a, b, c and d are in G.P. We have (a+bx)/(aโbx) = (b+cx)/(bโcx) = (c+dx)/(c โ dx) & we want to show that a, b, c, d are in G.P. Taking (a+bx)/(aโbx) = (b+cx)/(bโcx) = (c+dx)/(c โ dx) Applying componendo dividendo (a + bx + a โ bx)/((a + bx) โ(aโbx)) = (b + cx + (b โ cx))/(b + cx โ(b โ cx)) = (c + dx + (c โ dx))/(c + dx โ (c โ dx)) (a + a + bx โ bx)/(๐๐ฅ+ bx โ a + a ) = (b + b + cx โ cx)/(cx + cx โ ๐ + ๐) = (c + dx + c โ dx)/(dx + dx โ ๐ + ๐) (2๐+0)/(2๐๐ฅ+0) = (2๐ + 0)/(2๐๐ฅ + 0) = (2๐+0)/(2๐๐ฅ+0) 2๐/2๐๐ฅ = 2๐/2๐๐ฅ = 2๐/2๐๐ฅ ๐/๐๐ฅ = ๐/๐๐ฅ = ๐/๐๐ฅ 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

Miscellaneous

Misc 1

Misc 2

Misc 3 Important

Misc 4

Misc 5

Misc 6 Important

Misc 7 Important

Misc 8

Misc 9

Misc 10 Important

Misc 11

Misc 12

Misc 13 You are here

Misc 14 Important

Misc 15

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Misc 19 Important

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Misc 21 (i) Important

Misc 21 (ii)

Misc 22 Important

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Misc 24 Deleted for CBSE Board 2022 Exams

Misc 25 Important Deleted for CBSE Board 2022 Exams

Misc 26 Deleted for CBSE Board 2022 Exams

Misc 27

Misc 28 Important

Misc 29 Important

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Misc 32 Important

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.