SOLUTION: Find two consecutive positive integers such that the sum of their squares is 85. [You must use algebra to solve this, setting up an equation with a variable, and using algebra to s

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Question 67542: Find two consecutive positive integers such that the sum of their squares is 85. [You must use algebra to solve this, setting up an equation with a variable, and using algebra to solve for the variable.]
This one has me so confused. I need help, please????
Answer by 303795(602) About Me  (Show Source):
You can put this solution on YOUR website!
If the first number is x then the consecutive number will be x+1.
The squares of these two numbers add to 85 so
x%5E2+%2B+%28x%2B1%29%5E2=85
x%5E2+%2B+x%5E2+%2B+2x+%2B1=85
2x%5E2++%2B+2x+%2B+1+=+85
2x%5E2++%2B+2x+-+84+=0
Divide each side of the equation by 2
x%5E2++%2B+x+-+42+=0
factorise
%28x%2B7%29%28x-6%29+=0
So x=-7 or x=6
The problem states that the numbers are positive so x=6.
The consecutive numbers are therefore 6 and 7 (6%5E2%2B7%5E2=36%2B49=85)