Question

Divide 32 in the four parts which are the four terms of an AP such that the ratio of the product of the first and fourth terms is to the product of the
second and the third terms as 7:32.

Answer 1

Answer:

Step-by-step explanation:

Let the our parts are a-3d,a-d,a+d and a+3d.

Then by the given question, 

a-3d+a-d+a+d+a+3d=32

or, 4a=32

or, a=8 and

(a-3d)(a+3d)/(a-d)(a+d)=7/15

or, a²-9d²/a²-d²=7/15

or, 15a²-135d²=7a²-7d²

or, 15a²-7a²=-7d²+135d²

or, 8a²=128d²

or, 8×8²=128d²

or, d²=8×8×8/128

or, d²=4

or, d=+-2

∴, The four parts are:

when d=2

8-(3×2)=8-6=2

8-2=6

8+2=10

8+(3×2)=14

when d=-2

8-(3×-2)=8+6=14

8-(-2)=8+2=10

8+(-2)=8-2=6

8+(3×-2)=8-6=2