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) + 2ab =16
6 + ab + 2ab = 16
3ab = 10
ab = 10/3
a^2 + b^2 = 6 + ab
a^2 + ^2 - ab = 6
a^3 + b^3 = ( a + b) ( a^2 + b^2 - ab) = (4)(6) = 24
+182 
