The product of two consecutive positive odd numbers is 1,023. Find the numbers.

31, 33

Step-by-step explanation:

First find the prime factorization which is:

3*11*31 = 1023

if you multiply 3*11 you get 33

and the other number left over in the equation is 31

so you know that 31*33 = 1023 and they are consecutive odds so it works

31, 33

Step-by-step explanation:

Let x = smaller odd number.

Then the next greater consecutive odd number is x + 2.

Their product is x (x + 2).

Their product equals 1023.

x (x + 2) = 1023

x^2 + 2x = 1023

x^2 + 2x - 1023 = 0

(x + 33) (x - 31) = 0

x + 33 = 0 or x - 31 = 0

x = - 33 or x = 31

We discard the negative answer since we are told both numbers are positive.

x = 31

x + 2 = 33

The numbers are 31 and 33.