Divide 32 into 4 parts which are in AP such that the ratio of the product of the extremes to the product of the means is 7:5 .
If I'm interpreting your problem correctly, something is wrong in your problem.
Consider the sequence:
a-3d,a-d,a+d,a+3d
This is an arithmetic progression with constant difference 2d.
The product of the 2 outer terms is a^2 - 9d^2. The product of the 2 inner terms is a^2 - d^2.
Your requested ratio is:
which leads to
which is impossible.
Hello, prantik007!
Please check the problem for typos.
As stated, the situation is patently impossible.
Divide 32 into 4 parts which are in AP such that the ratio of the product
of the extremes to the product of the means is 7:5 .??
The four parts are: .
The product of the extremes is: .
The product of the means is: .
. . It is obvious that: .
So how can . ?