SOLUTION: The sum of the squares of two consecutive positive integers is 85. Find both integers. Im not how 2 set up the problem

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The sum of the squares of two consecutive positive integers is 85. Find both integers. Im not how 2 set up the problem      Log On


   

Question 77122: The sum of the squares of two consecutive positive integers is 85. Find both integers. Im not how 2 set up the problem
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the consecutive integers n and n+1
n%5E2+%2B+%28n%2B1%29%5E2+=+85
n%5E2+%2B+n%5E2+%2B+2n+%2B+1+=+85
2n%5E2+%2B+2n+-+84+=+0
n%5E2+%2B+n+-+42+=+0
I solved by completing the square
n%5E2+%2B+n+=+42
n%5E2+%2B+n+%2B+1%2F4+=+42+%2B+1%2F4
%28n+%2B+1%2F2%29%5E2+=+42.25
n+%2B+.5+=+6.5
n+=+6
n+%2B+1+=+7 these are the numbers
check answer
6%5E2+%2B+7%5E2+=+85
36+%2B+49+=+85
85+=+85
OK