Question

The sum of swuares of two consecutive positive integers is 313

Answer 1

1st consecutive = x
2nd consecutive = x+1
(x) square +(x+1) square = 313
x square + x square +1 + 2x = 313
2 x square +1 +2x = 313
2x square +2x - 312 = 0
x square + x - 156 = 0
x square + 13x -12x - 156 = 0
x ( x + 13 ) - 12 (x +13 ) = 0
(x + 13)(x-12) = 0
x = -13 and x = 12