Question

The sum of two natural numbers is 14 and the sum of their reciprocals is 7/24. Find the numbers​

Answer 1

Answer:

8,6

Step-by-step explanation:

8+6=14

1/8+1/6=14/48=7/24

Answer 2

Answer:

Numbers are 6 and 8

Step-by-step explanation:

Let them be x and y.

Then x+y = 14

Sum of their reciprocal

=1/x +1/y

=>(x+y)/xy=7/24

=>14/xy=7/24 ( put value of x+y=14)

=>14×24/7=xy

=>xy=48

since x + y = 14

therefore, x = 14 - y

(14 - y)(y) =48

=>14y-y^2 = 48

=>0 = y^2 - 14y + 48

=>0= y^2 - 6y - 8y + 48

=>0= y(y - 6) -8( y - 6 )

=>0= (y - 6) (y -8 )

So y can be 6 or 8.

Now put y = 6 then x = 8