SOLUTION: Find two consecutive positive integers such that the sum of their squares is 85. Please show work.

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Question 74285: Find two consecutive positive integers such that the sum of their squares is 85.
Please show work.
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Find two consecutive positive integers such that the sum of their squares is 85.
:
Let the 1st number be: x
Then the next consecutive number is: x+1
sum means: +
Squares means: ^2
is means: =
x%5E2%2B%28x%2B1%29%5E2=85
x%5E2%2B%28x%2B1%29%28x%2B1%29=85
x%5E2%2Bx%28x%2B1%29%2B1%28x%2B1%29=85
x%5E2%2Bx%28x%29%2Bx%281%29%2B1%28x%29%2B1%281%29=85
x%5E2%2Bx%5E2%2Bx%2Bx%2B1=85
2x%5E2%2B2x%2B1=85
2x%5E2%2B2x%2B1-85=85-85
2x%5E2%2B2x-84=0
2%28x%5E2%2Bx-42%29=0
2%28x%5E2%2Bx-42%29%2F2=0%2F2
x%5E2%2Bx-42=0
%28x%2B7%29%28x-6%29=0
x+7=0 or x-6=0
x+7-7=0-7 or x-6+6=0+6
x=-7 or x=6
We are only interested in positive integers, so throw out the -7.
The first integer is: x=6
The second integer is: x+1=6+1=7
:
Sanity Check:
If you added their squares would you get 85?
6%5E2%2B7%5E2=85
36%2B49=85
85=85
We seem to be on the right track.
Happy Calculating!!!!