+129850
x + 1/x = -5 (1)
square both sides and we have
x^2 + 2 + (1/x)^2 = 25 → x^2 + (1/x)^2 = 23 (2)
x^3 + (1/x)^3 can be factored as a sum of cubes thusly
(x + 1/x) ( x^2 - 1 + (1/x)^2 ) =
(x + 1/x) ( x^2 + (1/x)^2 - 1 ) sub (1) and (2) into this
(-5) ( 23 - 1) =
(-5) (22) =
-110
