SOLUTION: the sum of the squares of two consecutive even numbers is 244.find the integers.

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Question 36842: the sum of the squares of two consecutive even numbers is 244.find the integers.
Answer by vidhyak(98) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers be x , x+2
x^2 + (x+2)^2 = 244
x^2 + x^2 +4x +4 = 244
2x^2 +4x +4 = 244
2x^2 +4x -240 = 0

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B4x%2B-240+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A2%2A-240=1936.

Discriminant d=1936 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+1936+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+1936+%29%29%2F2%5C2+=+10
x%5B2%5D+=+%28-%284%29-sqrt%28+1936+%29%29%2F2%5C2+=+-12

Quadratic expression 2x%5E2%2B4x%2B-240 can be factored:
2x%5E2%2B4x%2B-240+=+2%28x-10%29%2A%28x--12%29
Again, the answer is: 10, -12. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B-240+%29