Question

112 is divided into four parts in A.P such that the product of
extremes is 128 less than the product of the other two. Find the four
parts
No Spam please !

Answer 1

Answer:

Let the 4 Parts be a-3d, a-d, a, a+d, a+3d

Now, on adding the above parts, we get :

a-3d+ a-d+ a+ a+d+ a+3d

=> 4a = 112

      a = 28 ...(i)

(a-3d)(a+3d) = (a-d)(a+d) - 128

 a^2 - 9d^2 =a^2 - d^2 - 128

         -8d^2 = -128

          8d^2 = 128

On further solving,

                                  d = (+ or -) 4

             Considering d = 4

a-3d = 16

a-d   = 24

a       = 28  (From (i))

a+d   = 32

a+3d = 40

Therefore, the four parts are : 16,24,28,32,40

Hope that Helps !