<PRE><B>Question 790617</B>
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

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