SOLUTION: Find two consecutive odd integers the sum of whose squares is 130

Question 107537This question is from textbook Algebra and Trigonometry Structure and Method book 2
: Find two consecutive odd integers the sum of whose squares is 130
This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If one of your odd integers is n, then the next consecutive odd integer is n+2.
Since the sum of the squares of these two integers is 130, you can say:

:Expand the binomial

:Collect terms and put the equation in standard form
:Factor out the 2

Now, you need to find two integers that have the following properties:
Their product is -63, and their sum is +2. Since the product is negative, we know that the two numbers are of opposite signs, and since their sum is positive, we know the larger of the two must be positive.

So, what are the factors of 63? Let's try 7 and 9. If we choose -7 and +9 we have a fit for the properties. -7 * 9= -63 and -7 + 9 = 2.
Therefore, the left hand expression factors to n - 7 and n + 9, so n = 7 or n=-9

That means that our first consecutive odd integer is either 7 or -9, so the second consecutive odd integer is either 9 or -7.

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