Question

Divide 32 into four parts which are in AP such that product of extremes is to the product of means is 7:15.

Answer 1

Divide 32 into four parts which are in AP such that product of extremes is to the product of means is 7:15.

Good question,

Here is your answer!

Let four parts be (a-3b), (a-b),(a+b) & (a+3b).

According to question,

=) a-3b + a - b + a+b+ a+3b = 32

=) 4a = 32

=) a = 32/4 = 8.

It is given,

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

=) a² - 9b²/a² - b² = 7/15

Put a= 8,

=) 128b² = 512

=) b² = 4

=) b = +-2

Hence four parts are 8-3*2 , 8-2, 8+2 & 8+3*2

= 2,6,10 & 14.

Answer 2

lets say the 4 numbers are: a-3d, a-d, a+d, a+3d

where sum of 4 terms = 32,

hence 4a = 32, implies a = 8;

according to question:

(8-3d)(8+3d)/(8-d)(8+d) = 7/15

solving we get answer: 2,6,10,14