Eqns; x - y = 3 ..........................(i)
xy = 27 ...........................(ii)
from eqn (ii)
x = 27/y
sub this value into eqn (i)
27/y - y = 3
27 - y^2 = 3y
y^2 + 3y - 27 = 0
from y = {-b +/- (b^2 -4ac)^1/2}/2a
y = {-3 +/- (9 + 108)}/2
y = (-3 +/ 10.82)/2
either
y = -6.91 ......... or........... 3.91
from { x = 27/y}
either
x = -3.91(for y = -6.91) .................. or ............... 6.91(fro y = 3.91)
(x + y)^3 = (-3.91 - 6.91)^3
= -1266.72
or
(x + y)^3 =(3.91 + 6.91)^3
=1266.72
therefore
(x + y)^3 = 1266.72 or -1266.72 {correct to 2dps}