SOLUTION: The sum of the squares of two consecutive integers is 685. Find the integers. I tried solving this myself and got 324 and 325 which is not the right answer, I'm not very good wi

Question 790617: The sum of the squares of two consecutive integers is 685. Find the integers.
I tried solving this myself and got 324 and 325 which is not the right answer, I'm not very good with word problems. Thank you in advance!
Found 2 solutions by rothauserc, stanbon:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
we are given the following
x^2 +(x+1)^2 = 685
x^2 +x^2+2x+1 = 685
2x^2 +2x = 684
x^2 +x = 342 and
x^2 +x -342 = 0
use quadratic equation to solve for x
x = (-1 + or - square root(1 - 4*1*(-342)) / 2
x = (-1 + or - 37) / 2
the problem does not state if our consecutive integers are positive or negative
x = 18 or -19
18^2 + 19^2 = 685
324 + 361 = 685
685 = 685
now
-19^2 + -18^2 = 685
361 + 325 = 685
so our integers are 18, 19, -19, -18

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The sum of the squares of two consecutive integers is 685. Find the integers.
--------
1st: x
2nd: x+1
------
Equation:
x^2 + (x+1)^2 = 685
x^2 + x^2 + 2x + 1 = 685
-----
2x^2 + 2x - 684 = 0
x^2 + x - 342 = 0
------
x = 18
x+1 = 19
=================
Cheers,
Stan H.
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