Divide 56 in four parts in A.P. such that the ratio of the product of their extremes (1st and 4th) to the
product of middle (

1 thought on “Divide 56 in four parts in A.P. such that the ratio of the product of their extremes (1st and 4th) to the<br />product of middle (”

1. Answer:

   Let 4 parts in AP be a, a +d, a+2d, a+3d

   It is given

   a+(a+d)+(a+2d)+(a+3d)=56

   4a+6d=56

   2a+3d=28

   {a×(a+3d)}/{(a+d)(a+2d)}

   Cross multiply then simplify

   a^2+3ad-10d^2=0

   Factorise by mid term splitting

   (a+5d)(a-2d)=0

   a=-5d

   a=2d

   put this value of a in equation

   2a+3d=28

   -10d+3d=28

   -7d=28

   d=-4

   a=20

   So AP 20, 16,12,8

   You will get another set when you take another value of d

   Reply