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.