Question

The product of two consecutive odd integers is $399$.

Find the numbers.

Short answer

The sets of consecutive odd integers are$\{-21,-19\},\{19,21\}$

Step-by-step solution

Step 1. Given

The product of two consecutive odd integers is$399$.

Step 2. Find two consecutive odd integers 

Let two consecutive odd integer as $n,n+2$

Product=$399$

$$\begin{gathered} n(n+2)=399 \\ {n}^2+2n-399=0 \\ {n}^2+21n-19n-399=0 \\ n(n+21)-19(n+21)=0 \\ (n+21)(n-19)=0 \end{gathered}$$

So,

$n=-21,19$

The first set of consecutive integer is

$$\begin{gathered} \{n,n+2\} \\ \{-21,-21+2\} \\ \{-21,-19\} \end{gathered}$$

The second set of consecutive integer is

$$\begin{gathered} \{n,n+2\} \\ \{19,19+2\} \\ \{19,21\} \end{gathered}$$

Step 3. Required answer

The sets of consecutive odd integers are$\{-21,-19\},\{19,21\}$