Question

product of two consecutive odd integers is 99 find the numbers

Answer 1

Hi !

Let the two consecutive odd integers be x and
x +2

Given :-

x(x+2) = 99

x² + 2x = 99

x² + 2x - 99 = 0

splitting the middle term :-

x² + 11x - 9x - 99 = 0

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

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

x = 9 , x = - 11


x = 9 is the value taken here :-

x = 9
x + 2 = 9 + 2 = 11

The no:s would be 9 and 11

Answer 2

let one of the odd numbers = a
second odd number = a+2

a(a+2)=99
a²+2a=99
a²+2a-99=0
a²+11a-9a-99=0
a(a+11)-9(a+11)=0
a+11=0. a-9=0
a=-11 a=9

a=9
since,odd number may not be in negative.

Therefore two odd numbers r 9,11