SOLUTION: How do you set up an equation to solve problems that have two consecutive odd/even positive integers adding up to a certain sum. For example, the sum of the square of two consecuti

Question 295508: How do you set up an equation to solve problems that have two consecutive odd/even positive integers adding up to a certain sum. For example, the sum of the square of two consecutive odd positive integers is 130, find the values of the two integers. I know that they're 7 and 9, but only through guess and check. How would I set up an equation to solve problems like that?
Found 2 solutions by Alan3354, edjones:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The numbers are n and n+2, or x and x+2

like that
You can solve the quadratic, and get 7&9, or -9 & -7
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But, if you're taking a timed test, do it like this:
130/2 = 65
square root of 65 =~ 8, between the 2 numbers.
--> 7 & 9
don't waste time

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Let the numbers be x and x+2
x^2+(x+2)^2=130
x^2+x^2+4x+4=130
2x^2+4x-126=0
x^2+2x-63=0
(x+9)(x-7)=0
x=7, x+2=9
.
Ed
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