SOLUTION: Please help me solve this problem: Find two consecutive positive integers such that the sum of their sraures is 85.

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Question 107287: Please help me solve this problem: Find two consecutive positive integers such that the sum of their sraures is 85.
Answer by Annabelle1(69) About Me  (Show Source):
You can put this solution on YOUR website!
did you mean sum of their squares?
if you did.....
let the first integer be x and the second (x+1)
sum of their square:
x%5E2%2B%28x%2B1%29%5E2
=x%5E2%2Bx%5E2%2B2x%2B1
=2x%5E2%2B2x%2B1
this is equal to 85
so we have
2x%5E2%2B2x%2B1=85
2x%5E2%2B2x%2B1-85=0
2x%5E2%2B2x-84=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B2x%2B-84+=+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=%282%29%5E2-4%2A2%2A-84=676.

Discriminant d=676 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+676+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+676+%29%29%2F2%5C2+=+6
x%5B2%5D+=+%28-%282%29-sqrt%28+676+%29%29%2F2%5C2+=+-7

Quadratic expression 2x%5E2%2B2x%2B-84 can be factored:
2x%5E2%2B2x%2B-84+=+2%28x-6%29%2A%28x--7%29
Again, the answer is: 6, -7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B2%2Ax%2B-84+%29


if your only positive answer is six, the 2 consecutive numbers are 6 and 7