Question

The product of two consecutive odd numbers is 255.Find the numbers.

Short answer

Therefore, the consecutive odd numbers are 15 and 17 .

Step-by-step solution

Given information

The given information states that the product of two consecutive odd numbers is 255.

Take one number is x and other is x+2.

$$\begin{gathered} \left(\mathrm{x}\right)\left(\mathrm{x}+2\right)=255 \\ \mathrm{Simplify}\mathrm{the}\mathrm{equation} \\ {\mathrm{x}}^2+2\mathrm{x}=255 \\ {\mathrm{x}}^2+2\mathrm{x}-255=0 \end{gathered}$$

Using quadratic formula

$$\begin{gathered} x^2+2x-255=0 \\ \mathrm{whereas}\mathrm{a}=1,\mathrm{b}=2\mathrm{and}\mathrm{c}=-255 \\ \mathrm{x}=\frac{-2\pm \sqrt{2^2-4\left(1\right)\left(-255\right)}}{2\left(1\right)} \\ \mathrm{x}=\frac{-2\pm \sqrt{4+1020}}{2} \\ \mathrm{x}=\frac{-2\pm \sqrt{1024}}{2} \\ \mathrm{x}=\frac{-2\pm 32}{2}\left(\mathrm{take}\mathrm{positive}\mathrm{value}\mathrm{only}\right) \\ \mathrm{x}=\frac{-2+32}{2} \\ \mathrm{x}=\frac{30}{2} \\ \mathrm{x}=15 \\ \mathrm{x}+2=15+2 \\ =17 \end{gathered}$$