The difference of two natural numbers is 5 and the difference of their reciprocals is 5 /14 . Find the numbers.Submitted on 8/3/2024 | Answered by Vandana Rana

Answer :

Let the two natural numbers be x and y y>x
According to question
y
−
x
=
5
.....(1)
1/
x
−
1/
y
=
5_
14
....(2)
From( 1.)
y
=
x
+
5
Putting the value of y in eqn. (2)
1/
x
−
1/(
x
+
5)
=
5/
14
=>
(x
+
5
−
x)
/
(
x^{2}
+
5x
)
=
5/
14
=>
5/(x^{2}+5x)=5/14
=>
x^{2}
+
5
x
−
14
=
0
=>
x^{2}
+
7x
−
2x
−
14
=
0
=>
=>
x
(
x
+
7
)
−
2
(
x
+
7
)
=
0
=>
(
x
+
7
)
(
x
−
2
)
=
0
Either
x
+
7
=
0
=>
x
=
−
7
Not acceptable because -7 is not natural number
Or,
x
−
2
=
0
=>
x
=
2
So, the first number is 2
Other number
=
x
+
5
=
2
+
5
=
7
so the numbers are 7 and 2