Question

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

Answer 1

Let the required natural numbers be x and `(8-x)` 

It is given that the product of the two numbers is 15 

∴ `x(8-x)=15` 

⇒` 8x-x^2=15` 

⇒`x^2-8x+15=0` 

⇒`x^2-5x-3x+15=0` 

⇒`x(x-5)-3(x-5)=0` 

⇒`(x-5)(x-3)` 

⇒`x-5=0  or  x-3=0` 

⇒`x=5  or  x=3` 

Hence, the required numbers are 3 and 5.