Question

what is the sum of reciprocal of x when 25 observations give​

Answer 1

Step-by-step explanation:

Let x and y be the two numbers. Then:

x + y = 25

1/x + 1/y = 1/4

Multiply the second equation by xy to get:

y + x = xy/4

The left sides of the two equations are now equal, so the right sides must be as well, giving:

xy =100

At this point I just tried a few factors of 100. Simple trial and error quickly conformed the answer as 5 and 20.

Alternatively, substituting x = 100/y in the first equation and multiplying through by y yields a quadratic whose solution gives the same result:

y^2 - 25 y + 100 = 0