Answer:

let the two numbers be x and y

x+y=8

thus, x=8-y

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

Substituting the value of x:

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

15((y+8-y)/(y×(8-y))=8

15(8/8y-y square)=8

15=8y-y square

-y square+8y-15=0

-y square+3y + 5y - 15 =0

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

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

if 5-y=0

-y=-5

y=5

x=8-y=3

if y-3=0

y=3

x=8-y=5

Hence,either way the two numbers are 3 and 5.