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

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Question 252827: The sum of the squares of two positive consecutive integers is 130. Find the integers. Only an algebraic solution will be accepted.
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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