Question 416350
Let the consecutive integers be n, n+1, and n+2
We have {{{n^2 + (n+1)^2 +(n+2)^2 = 1877}}}
Multiplying terms gives {{{n^2 + n^2 + 2n + 1 + n^2 + 4n + 4 = 1877}}}
Collecting like terms and putting in the proper form gives
 {{{ 3n^2 + 6n - 1872 = 0 }}}
Applying the quadratic formula we get 
{{{n = (-6 +- sqrt(6^2 - 4*3*(-1872) ))/(2*3)}}} -> {{{(-6 +- 150)/6}}}
This gives n = -26, 24
So one set of consecutive integers is 24,25,26 and the other is -26,-25,-24