The real numbers $a$ and $b$ satisfy $a - b = 1$ and $a^3 - b^3 = 1.$
(a) Find all possible values of $ab.$ (b) Find all possible values of $a + b.$ (c) Find all possible values of $a$ and $b.$
a^3 - b^3 = (a - b) (a^2 + ab + b^2)
1 = 1 ( a^2 + ab + b^2)
1 = a^2 + ab + b^2
a b ab a + b
-2/sqrt 3 1/sqrt 3 -2/sqrt3 -1 /sqrt 3
2/sqrt 3 -1/sqrt 3 1/sqrt 3
1 0 0 1
-1 0 -1
-1 1 -1 0
0 1
0 -1
1 -1
+1025 
