SOLUTION: The sum of the squares of two consecutive natural numbers is 85. Determine the number.

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Question 446477: The sum of the squares of two consecutive natural numbers is 85. Determine the number.
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equation:x%5E2%2B%28x%2B1%29%5E2=85. Set the equation to zero:
2x%5E2%2B2x-84=0=>x%5E2%2Bx-42=0=>%28x-6%29%28x%2B7%29=0
The solution is: x=-7 which is rejected because it is not natural number, and
x=6 which is the right solution.
Answer:Two consecutive natural numbers are 6 and 7.