Question

. The sum of two numbers is 8 and the sum of the
reciprocals is 8/15
. Find the numbers by simultaneous equations​

Answer 1

Let the numbers be x and y

ATQ

x + y = 8 ---(1) and 1/x + 1/y = 8/15

Now,

1/x + 1/y = 8/15

=> (x + y)/xy = 8/15

=> 8/xy = 8/15

=> xy = 15

Then, we can use

(x - y)² = (x + y)² - 4xy

(x - y)² = (8)² - 4(15)

x - y = ± 2

=> x - y = 2 ---(2) or x - y = -2 ---(3)

Solving equations (1), (2) & (3), we'll get,

x = 5 and y = 3 or x = 3 and y = 5

Both these solutions are one and the same. In this case, order of these numbers doesn't matter.

So, 5 and 3 are the required numbers.

Hope, it'll help you.....