The sum of two natural numbers is 8 and their product is 15. Find the numbers.

Let the required natural number be x and (8 - x)

their product is 15

x(8 - x) = 15

8x –x^{2} = 15

x^{2} - 8x + 15 = 0

Using the splitting middle term - the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation a = 1 b = - 8 c = 15

= 1.15 = 15

And either of their sum or difference = b

= - 8

Thus the two terms are - 5 and - 3

Sum = - 5 - 3 = - 8

Product = - 5. - 3 = 15

x^{2} - 5x - 3x + 15 = 0

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

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

x = 5 or x = 3

Hence the required natural numbers are 5 and 3

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