Question 289
Lets call our integers i and j. Any 2 consecutive odd integers will always be 2 apart, so we can first say that:

{{{j = i + 2}}}

From the remainder of the question, we can say that:

{{{i^2 + 3j = 24}}}

Substituting the first equation in the second gives:

{{{i^2 + 3(i + 2) = 24}}}

Rearranging and expanding brackets gives us a quadratic equation:

{{{i^2 + 3i - 18 = 0}}}

Factorising it gives:

{{{(i - 3)(i + 6) = 0}}}

Therefore i is either 3 or -6. Since i is odd according to the original question, i must be 3.

Since j is the following odd integer after i, j must be 5.

Result:

The 2 integers are 3 and 5.