uestion 1: ) If x,y and z are in continued proportion, prove that (x+y) (y+z)=x/z​

Question

uestion 1:
) If x,y and z are in continued proportion, prove that
(x+y)
(y+z)=x/z​

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Julia 3 weeks 2021-10-04T01:35:29+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-10-04T01:36:42+00:00

    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

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