SOLUTION: how do i find two consecutive positive integers such that the sum of their squares is 85?

Question 79243: how do i find two consecutive positive integers such that the sum of their squares is 85?
Found 2 solutions by stanbon, sprolden:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
how do i find two consecutive positive integers such that the sum of their squares is 85?
--------
The consecutive integers are "x" and "x+1".
EQUATION:
x^2+(x+1)^2=85
x^2+x^2+2x+1=85
2x^2+2x+1=85
2x^2+2x=84
x^2+x=42
x^2+x-42=0
(x+7)(x-6)=0
The only positive answer is x=6; then x+1=7
============
Cheers,
Stan H.

Answer by sprolden(40) (Show Source): You can put this solution on YOUR website!
how do i find two consecutive positive integers such that the sum of their squares is 85?
1- The perfect squares just before 85 are the following:
4, 9, 16, 25, 36, 49, 64, 81
2- Looking at your numbers, you can add 36 and 49 to get 85.
3- The square root of 36 is 6 and the square root of 49 is 7. Therefore, two consecutive integers whose sum of their squares is 85 are 6 and 7.
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