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sum of two natural numbers is eight and sum of their reciprocals is 8/15. find the two numbers?
let the no. be x and y
x+y=8 .......(1)
1/x + 1/y=8/15 ................(2)
i.e. (x+y)/(x*y) = 8/15
i.e x*y = 15 .......(put x+y=8 from 1)
i.e y=15/x........(3)
put (3) in (1) to get (x^2)-8x+15=0
solve to get x=3&y=5 or x=5&y=3
so the no. are 3 & 5
let 1 no =x
----2----=y
x+y=8 ------eg. 1
; 1/x+1/y = 8/15 i.e (x+y)/xy=8/15
thus xy=15 now from eq.1, x=8-y putting here in this eq.
(8-y)*y=15
8y-y2=15 = y2-8y+15=0
solving we get y=5 or y=3
so nos. are 5,3
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