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.
[tex]x(x+2)=99[/tex]
[tex]x^2+2x-99=0[/tex]
Splitting the middle term, we get
[tex]x^2+11x-9x-99=0[/tex]
[tex]x(x+11)-9(x+11)=0[/tex]
[tex](x+11)(x-9)=0[/tex]
[tex]x=-11,9[/tex]
If x=-11, then second odd integer is
[tex]-11+2=-9[/tex]
If x=9, then second odd integer is
[tex]9+2=11[/tex]
Therefore, the two consecutive odd integers are either -11, -9 or 9, 11.
