Question

Divide 96 into 4 parts which are in ap and the ratio between the product of their means to product of their extermes is 15:7

Answer 1

let 96 be divided as a-3d , a-d ,a+d and a+3d

A/Q,

=> a-3d+a-d+a+d+a+3d = 96

=> 4a = 96

=> a = 24

and

$= > \frac{(a - d)(a + d)}{(a - 3d)(a + 3d)} = \frac{15}{7} \\ \\ = > \frac{ {a}^{2} - {d}^{2} }{ {a}^{2} - 9 {d}^{2} } = \frac{15}{7} \\ \\ = > 7 {a}^{2} - 7 {d}^{2} = 15 {a}^{2} - 135 {d}^{2} \\ \\ = > 8{a}^{2} = 128 {d}^{2} \\ \\ = > { d}^{2} = \frac{8 \times 24 \times 24}{128} \\ \\ = > d = \sqrt{ \frac{ {24}^{2} }{16} } \\ \\ = > d = 6$

the required no.s are 6, 18 , 30 , and 42