Conditional identity consisting of AP and GP

AI Thread Summary
The discussion revolves around proving the equation (xb÷xc)(yc÷ya)(za÷zb)=1, given that x, y, z are in geometric progression (GP) and a, b, c are in arithmetic progression (AP). Participants emphasize the importance of utilizing the properties of GP and AP in the proof. One user acknowledges a lack of thorough consideration before posting their attempt at a solution. The conversation highlights the need for careful analysis of the relationships between the terms in both progressions. Overall, the thread underscores the significance of understanding mathematical concepts before attempting to solve related problems.
rama
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Homework Statement


x,y,z are three terms in GP and a,b,c are three terms in AP
prove that (xb÷xc)(yc÷ya)(za÷zb)=1

Homework Equations


The Attempt at a Solution


(xb-c)(yc-a)(za-b)

since x y z are in GP
xb-c÷yc-a=yc-a÷za-b
(xb- c)(za-b)=yc-a(yc-a)
 
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rama said:

Homework Statement


x,y,z are three terms in GP and a,b,c are three terms in AP
prove that (xb÷xc)(yc÷ya)(za÷zb)=1


Homework Equations





The Attempt at a Solution


(xb-c)(yc-a)(za-b)

since x y z are in GP
xb-c÷yc-a=yc-a÷za-b
(xb- c)(za-b)=yc-a(yc-a)

You are given that x, y, and z are in geometric progression. Did you use that fact in your work?

Also, a, b, and c are in arithmetic progression. Did you use that fact in your work?
 
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got it thank you, I seem to be posting here without thinking hard
next time I won't post without thinking out all options sorry
 

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