Integers for 199694

Question

The sum of the squares of three integers is 199694. Determine the integers

Answer 1

257,258, 259, square each, sum them, = 199694

x^2 + (x+1)^2 +(x+2)^2 = 199694

x^2 + x^2 + 2x + 1 +x^2 + 4x + 4 = 199694

3x^2 + 6x - 199689 = 0

x^2 +2x 66,563 = 0

(x-257)(2+259) = 0

x = 257 or -259

the 3 consecutive integers are 257, 258 and 259

or -259, -258 and -257

257^2 + 258^2 + 259^2

= 66049 + 66564 + 67081

= 199694

if you can't factor the quadratic, use the quadratic formula or complete the square

but another way is if you just take the square root of 66563 = virtually 258, which is the middle number of the 3 consecutive integers

Odds are the problem meant to say "consecutive integers" but "consecutive" got left out.

If you really wanted any 3 integers, including non-consecutive integers squared there may be other solutions