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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