Question

If X,y,z are in continued proportion
then show that.
X-y upon x-z is equal to y upon y+z​

Answer 1

x,y,z are in continued proportion, that is

y

x

=

z

y

(1)

then,y

2

=xz

Now,

(y+z)

2

(x+y)

2

=

z

2

(

z

y

+1)

2

y

2

(

y

x

+1)

2

=

z

2

(

y

x

+1)

2

y

2

(

y

x

+1)

2

( from (1)

y

x

=

z

y

)

=

z

2

y

2

=

z

2

xz

=

z

x