Question

The sum of two natural numbers is 8 an d the sum of their reciprocals is 8/15. Find the numbers.

Answer 1

Answer:

a=3, b= 5 or a=5, b =3

Step-by-step explanation:

Let a and b be two natural numbers.

a+b = 8

1/a+1/b = 8/15

a+b/ab = 8/15

8/ab = 8/15

ab = 15.

a=3, b= 5 or a=5, b =3

Answer 2

Answer:

Step-by-step explanation:

x and (8-x) are the numbers.

1/x+1/(8-x)=8/15

(8-x+x)/8x-x²=8/15

8 in the numerator can be cancelled.

1/8x-x²=1/15

Cross multiply

15=8x-x²

x²-8x+15=0

x²-3x-5x+15=0

x(x-3)-5(x-3)=0

(x-3)(x-5)=0

Therefore

x= 3 or 5

Hope this helps you.

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