Question

the sum of 2 natural numbers is 8. Determine the numbers if sum of their reciprocals is 8/15​

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.

Ignore spell Mistakes

Answer 2

Answer:

let the numbers be x and y

x+y =8

x =8-y

1/x + 1/y = 8/15

8/xy = 8/15

xy =15

y(8-y) = 15

8y -y^2 =15

y^2 -8y + 15=0

y^2 - 5y -3y +15 =0

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

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

y =5 or y =3

when y =5

then x = 8-5 = 3

when y =3

then x = 8-3 = 5