SOLUTION: Find two consecutive odd integers such that the square of the first, added to 3 times the second, is 24.

Question 289: Find two consecutive odd integers such that the square of the first, added to 3 times the second, is 24.
Answer by arden42(16) (Show Source): You can put this solution on YOUR website!
Lets call our integers i and j. Any 2 consecutive odd integers will always be 2 apart, so we can first say that:

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

Substituting the first equation in the second gives:

Rearranging and expanding brackets gives us a quadratic equation:

Factorising it gives:

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.
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