Question

Divide 40 into four parts, which are in A.P. such that the ratio of product of extremes to the
product of means is 3?​

Answer 1

Step-by-step explanation:

Given  

Divide 40 into four parts, which are in A.P. such that the ratio of product of extremes to the product of means is 2: 3?

• Let the four parts in A.P be a – 3d, a-d, a + d, a + 3d
• So a-3d + a – d + a + d + a + 3d = 40
• 4a = 40
• Or a = 10
• Now the four parts are 10 – 3d, 10 – d, 10 + d, 10 + 3d.
• Ratio of product of extremes to the product of means is 2:3
• So (10 – 3d)(10 + 3d) / (10 – d)(10 + d) = 2/3
• This is in the form of (a – b)(a + b) = a^2 – b^2  
•     So 100 – 9d^2 / 100 – d^2 = 2/3
•         300 – 27d^2 = 200 – 2d^2
•     25 d^2 = 100
•  So d^2 = 4
• Or d = ± 2

Therefore the four parts will be 4, 8,12, 16 or 16,12,8,4

Reference link

https://brainly.in/question/7733478