SOLUTION: The sum of the squares of two positive consecutive integers is 130. Find the integers. Only an algebraic solution will be accepted.

Question 252827: The sum of the squares of two positive consecutive integers is 130. Find the integers. Only an algebraic solution will be accepted.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
let n= the first integer and n+1= the second
n^2+(n+1)^2=130
n^2+n^2+2n+1=130
2n^2+2n=129
there are no integer roots
Something is wrong with problem.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1036 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 7.54673846971554, -8.54673846971554. Here's your graph:

perhaps you mean consecutive even or consecutive odd
first =n second n+2
n^2+(n+2)^2=130

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1024 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 7, -9. Here's your graph:

that does work
we discard the negative answer -9
7^2+9^2
49 +81=130
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