fraction problem

[kitty]

hi i am unable to solve this problem ,,,


if x ,y ,z are in continued proportion

prove that (x+y)^2/(y+z)^2=x/z

 

[daon2]

I had to google "continued proportion".

I don't know what you already know, you have shown no work. Am I to assume you don't know \(\displaystyle (x+y)^2=x^2+2xy+y^2\)?

 

[kitty]

i know (x+y)^2=x^2 +y^2+2xy

but this problem is where its told they are in continued proportion meaning x/y=y/z


and i am unable to do the above prove

 

[daon2]

i know (x+y)^2=x^2 +y^2+2xy

but this problem is where its told they are in continued proportion meaning x/y=y/z

z=y^2/x

and i am unable to do the above prove

Hint: \(\displaystyle y^2=xz\). Make some substitutions and do some factoring.