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

Are you in **school**? Do you **love Teachoo?**

We would love to talk to you! Please fill this form so that we can contact you

Miscellaneous

Misc 1
Deleted for CBSE Board 2023 Exams

Misc 2 Deleted for CBSE Board 2023 Exams

Misc 3 Important Deleted for CBSE Board 2023 Exams

Misc 4 Deleted for CBSE Board 2023 Exams

Misc 5 Deleted for CBSE Board 2023 Exams

Misc 6 Important Deleted for CBSE Board 2023 Exams

Misc 7 Important

Misc 8

Misc 9

Misc 10 Important

Misc 11

Misc 12

Misc 13 You are here

Misc 14 Important

Misc 15 Deleted for CBSE Board 2023 Exams

Misc 16 Important Deleted for CBSE Board 2023 Exams

Misc 17

Misc 18

Misc 19 Important

Misc 20

Misc 21 (i) Important Deleted for CBSE Board 2023 Exams

Misc 21 (ii) Deleted for CBSE Board 2023 Exams

Misc 22 Important Deleted for CBSE Board 2023 Exams

Misc 23 Important Deleted for CBSE Board 2023 Exams

Misc 24 Deleted for CBSE Board 2023 Exams

Misc 25 Important Deleted for CBSE Board 2023 Exams

Misc 26 Deleted for CBSE Board 2023 Exams

Misc 27 Deleted for CBSE Board 2023 Exams

Misc 28 Important Deleted for CBSE Board 2023 Exams

Misc 29 Important

Misc 30 Deleted for CBSE Board 2023 Exams

Misc 31 Important

Misc 32 Important Deleted for CBSE Board 2023 Exams

Last updated at May 29, 2018 by Teachoo

Misc 13 If , (a+bx)/(aβbx) = (b+cx)/(bβcx) = (c+dx)/(aβdx) (x β 0)then show that a, b, c and d are in G.P. Introduction Componendo dividendo If π₯/π¦ = π/π Applying componendo dividendo (π₯ + π¦)/(π₯ β π¦) = (π + π)/(π β π) Eg: Taking 1/2 = 4/8 (1+ 2)/(1 β 2) = (4 + 8)/(4 β 8) 3/(β1) = 12/(β4) -3 = -3 Misc 13 If , (a+bx)/(aβbx) = (b+cx)/(bβcx) = (c+dx)/(aβdx) (x β 0)then show that a, b, c and d are in G.P. We have (a+bx)/(aβbx) = (b+cx)/(bβcx) = (c+dx)/(c β dx) & we want to show that a, b, c, d are in G.P. Taking (a+bx)/(aβbx) = (b+cx)/(bβcx) = (c+dx)/(c β dx) Applying componendo dividendo (a + bx + a β bx)/((a + bx) β(aβbx)) = (b + cx + (b β cx))/(b + cx β(b β cx)) = (c + dx + (c β dx))/(c + dx β (c β dx)) (a + a + bx β bx)/(ππ₯+ bx β a + a ) = (b + b + cx β cx)/(cx + cx β π + π) = (c + dx + c β dx)/(dx + dx β π + π) (2π+0)/(2ππ₯+0) = (2π + 0)/(2ππ₯ + 0) = (2π+0)/(2ππ₯+0) 2π/2ππ₯ = 2π/2ππ₯ = 2π/2ππ₯ π/ππ₯ = π/ππ₯ = π/ππ₯ 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