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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 $b.$

 Feb 28, 2024
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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. 

 Feb 28, 2024

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