let the integers be x and y you have x+y=-17 ---------(1) xy=52 ---------(2) from eqn (1) x=-17-y --------(3) , so subsitute eqn (3) in to eqn(2) (-17-y)y=52 -17y-y²=52 : -y²-17y-52=0 same as y²+17y+52=0 y²+13y+4y+52=0 y(y+13)+4(y+13)=0 (y+4)(y+13)=0 therefore y=-4 or -13 now substitute y=-4 or -13 in eqn (3) x=-17-(-4) or -17-(-13) x= -13 or -4 so when x=-13 ,y=-4 and when x=-4 ,y=-13
