Question

Find two consecutive odd integers whose product is 99.​

Answer 1

Given:

Product of two consecutive odd integers is 99.

To find:

The two consecutive odd integers.

Solution:

Let the two consecutive odd integers are x and (x+2).

Product of two consecutive odd integers is 99.

`x(x+2)=99`

`x^2+2x-99=0`

Splitting the middle term, we get

`x^2+11x-9x-99=0`

`x(x+11)-9(x+11)=0`

`(x+11)(x-9)=0`

`x=-11,9`

If x=-11, then second odd integer is

`-11+2=-9`

If x=9, then second odd integer is

`9+2=11`

Therefore, the two consecutive odd integers are either -11, -9 or 9, 11.