Let a and b be complex numbers. If a + b = 4 and a^2 + b^2 = 6 + ab, then what is a^3 + b^3?
a + b = 4
square both sides
a^2 + 2ab + b^2 =16 → a^2 + b^2 = 16 - 2ab
a^2 + b^2 = 6
So
6 = 16 - 2ab
-10 = -2ab
5 = ab
-5 = -ab
a^3 + b^3 =
(a + b) ( a^2 + b^2 - ab) =
(4) (6 - - 5)
(4) (11) =
44
+657 
