Question

The sum of two naturals number is 8 and sum of their reciprocals is 8/15. find the numbers

Answer 1

the numbers are 3 & 5

Answer 2

Answer:

3 and 5

Step-by-step explanation:

Let the two natural numbers be x and y

Since we are given that the sum of these two natural numbers is 8

⇒$x+y=8$   --1

Now we are given that the sum of their reciprocals is $\frac{8}{15}$

⇒$\frac{1}{x}+\frac{1}{y}=\frac{8}{15}$

⇒$\frac{y+x}{xy}=\frac{8}{15}$

Using 1

⇒$\frac{8}{xy}=\frac{8}{15}$  --2

Substitute the value of y from 1 in 2

⇒$\frac{8}{x(8-x)}=\frac{8}{15}$

⇒$15=x(8-x)$

⇒$15=8x-x^2$

⇒$x^2-8x+15=0$

⇒$x^2-3x-5x+15=0$

⇒$x(x-3)-5(x-3)=0$

⇒$(x-3)(x-5)=0$

⇒$x=3,5$

when x = 3

So, x+y=8

3+y=8

y=5

when x = 5

So, x+y=8

5+y=8

y=3

Hence the numbers are 3 and 5