Question

The product of two consecutive positive odd integers is 255. what are the integers?

Answer 1

Let the smaller odd positive integer be n.
Then
n(n+2)=255
solve by expanding to quadratic equation n^2+2n-255=0, reject negative root, or
by trial and error: sqrt(255)=15.97 =16, so the odd integers should be 15, 17.
Check: 15*17=255 ....correct!!!

Alternatively, let the even number sandwiched between the odd integers be x.
Then
(x+1)(x-1)=255
x^2-1=255
x^2=255+1=256
x=sqrt(256)=16
so the required odd integers are 16-1=15, and 16+1=17.

Your choice!!