Question

The sum of two natural numbers is 8 and their product is 15. Find the numbers. [CBSE 2012]

Answer 1

Let the required natural numbers be x and (8 − x).

It is given that the product of the two numbers is 15.
$$\begin{gathered} \therefore x\left(8-x\right)=15 \\ \Rightarrow 8x-x^2=15 \\ \Rightarrow x^2-8x+15=0 \\ \Rightarrow x^2-5x-3x+15=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow x\left(x-5\right)-3\left(x-5\right)=0 \\ \Rightarrow \left(x-5\right)\left(x-3\right)=0 \\ \Rightarrow x-5=0\mathrm{or}x-3=0 \\ \Rightarrow x=5\mathrm{or}x=3 \end{gathered}$$

Hence, the required numbers are 3 and 5.