If a + b = 1 and a^2 + b^2 = 2, then find a^3 + b^3.
a + b = 1
Square both sides of this
a^2 + 2ab + b^2 = 1
(a^2 +b^2) + 2ab = 1
(2) + 2ab = 1
2ab = -1
ab = -1/2
-ab =1/2
a^3 + b^3 = (a + b) (a^2 - ab + b^2) = (a + b) [ (a^2 + b^2 ) + - ab) = (1) [ 2 +1/2] = 5/2
