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( ax/a+b ) = ( by/y+b ) = (cz/z+b ) & x, y, z, are in H.P. then a, b, c, are in 1) A.P. 2) G.P. 3) H.P. 4) None

( ax/a+b ) = ( by/y+b ) = (cz/z+b ) & x, y, z, are in H.P. then a, b, c, are in


1) A.P.


2) G.P.


3) H.P.


4) None

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear Mayank

( ax/x+b ) = ( by/y+b ) = (cz/z+b )

let

 ( ax/x+b ) = ( by/y+b ) = (cz/z+b ) =1/k

so x +b =axk   or    x =b/(ak-1)

 

   y+ b  =byk   or  y = b/(bk-1)

 

  z+b= czk   or   z =b/(ck-1)

 

 x ,y,z  are in H.P

or   1/x  ,1/y ,1/z   are in AP

or (ak-1)/b ,(bk-1)/b ,(ck-1)/b  are in AP

or (ak-1) ,(bk-1) ,(ck-1)  are in AP

or (ak) ,(bk1) ,(ck)  are in AP

or  a,b,c   are in AP

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Badiuddin

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