SOLUTION: The Sum of the squares of two consecutive positive intergers is 85.Find the Integers.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: The Sum of the squares of two consecutive positive intergers is 85.Find the Integers.      Log On


   

Question 212038: The Sum of the squares of two consecutive positive intergers is 85.Find the Integers.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the first positive integer, the x+1 = the next consecutive positive integer. The sum of the squares of these is 85.
x%5E2%2B%28x%2B1%29%5E2+=+85 Simplify.
x%5E2%2B%28x%5E2%2B2x%2B1%29+=+85
2x%5E2%2B2x+%2B1+=+85 Subtract 1 from both sides.
2x%5E2%2B2x+=+84 Divide both sides by 2.
x%5E2%2Bx+=+42 Subtract 42 from both sides.
x%5E2%2Bx-42+=+0 Factor the trinomial.
%28x%2B7%29%28x-6%29+=+0
%28x%2B7%29+=+0 or %28x-6%29+=+0 so...
x+=+-7 or x+=+6 Ignore the negative solution.
x+=+6
The two integers are: 6 and 7