Q. 325.0( 1 Vote )

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

Answer :

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

their product is 15


x(8 - x) = 15


8x –x2 = 15


x2 - 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


x2 - 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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