+1036 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 $b.$
+184 Try writing a in terms of b or b in terms of a to solve the equation. Like: a = b + 1. Then just replace it: a^3 - b^3 = (b-1)^3 - b^3 = 1. Expand, simplify, solve.
