Question

the sum of the two number is 8. find the number if the sum of their reciprocal is 8/15

Answer 1

Let the numbers be x and y.

x+y = 8

x = 8-y ----------(1)

Their reciprocals be 1/x and 1/y.

1/x+1/y = 8/15

y+x/xy = 8/15

We know y+x = 8 and according to equation 1,

8/8-y² = 8/15

y²-8y+15 = 0

(y-3)(y-5) = 0

y = 3 or 5

x = 5 or 3

Numbers will be 3 , 5