# How do you find 2 positive consecutive odd integers whose product is 483?

Jan 23, 2016

21 and 23

#### Explanation:

let n be an odd integer.

Then the next consecutive odd number will be n + 2. Odd

integers are separated by 2 ( 1 , 3 , 5 ,7 , 9......)

The product of n and n+ 2 = n(n + 2 ) =483

(distribute the brackets )

hence : ${n}^{2} + 2 n - 483 = 0$

To factor require 2 numbers that multiply to give - 483 and sum

to give +2. These are 23 and - 21 .

check : 23 # xx ( - 21 ) = - 483 and 23 - 21 = 2

so (n + 23 )( n - 21 ) = 0

$\Rightarrow n = - 23 \mathmr{and} n = 21$

Now n ≠ - 23 so n = 21 and n + 2 = 21 + 2 = 23