Question

the sum of two natural numbers is 8 and the sum of their reciprocals is 8/15 find the numbers

Answer 1

Let one number be X. The other number be Y.

GIVEN,

X+Y=8

X=8-Y ---------------(1)

1/X+1/Y=8/15

BY SIMPLIFING 1/X+1/Y=8/15 WE GET,

(X+Y)/XY=8/15

FROM (1) WE GET,

8/8Y-Y2=8/15

Y2-8Y+15=0

(Y - 3)(Y - 5) = 0

Y = 3 or 5

WE KNOW THAT X+Y=8

When Y=5, X=3

When Y = 3, X = 5

Thus, the two numbers are 3 and 5.

Answer 2

Let the 1st no. be x

x+y = 8
x=8-y---------(1)
1/x+1/y= 8/15
by simplifying 1/x+1/y= 8/15 we get,
(x+y)/xy=8/15