SOLUTION: One positive integer is 3 less than twice another. The sum of their squares is 698. Find the integers.

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Question 1008836: One positive integer is
3 less than twice another. The sum of their squares is
698. Find the integers.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
One positive integer is 3 less than twice another. The sum of their squares is
698. Find the integers.
----
x^2 + (2x-3)^2 = 698
5x^2 - 12x - 689 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-12x%2B-689+=+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=%28-12%29%5E2-4%2A5%2A-689=13924.

Discriminant d=13924 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--12%2B-sqrt%28+13924+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+13924+%29%29%2F2%5C5+=+13
x%5B2%5D+=+%28-%28-12%29-sqrt%28+13924+%29%29%2F2%5C5+=+-10.6

Quadratic expression 5x%5E2%2B-12x%2B-689 can be factored:
5x%5E2%2B-12x%2B-689+=+%28x-13%29%2A%28x--10.6%29
Again, the answer is: 13, -10.6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-12%2Ax%2B-689+%29

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--> 13 & 23