Question

8. Sum of two natural numbers is 8 and sum of their reciprocals is
-
8
find the numbers.
15
If the​

Answer 1

Step-by-step explanation:

the numbers be x and 8−x

⇒

x

1

+

8−x

1

=

15

8

⇒

x(8−x)

8−x+x

=

15

8

⇒

x(8−x)

8

=

15

8

⇒

x(8−x)

1

=

15

1

⇒x(8−x)=15

⇒x

2

−8x+15=0

⇒x

2

−5x−3x+15=0

⇒x(x−5)−3(x−5)=0

⇒x−5=0 or x−3=0

When x=3, the numbers are 3 and 8−3=5

When x=5, the numbers are 5 and 8−5=3

Hence the required numbers are 3,5