Find all real numbers \(a\) such that the equation \(x^3 - ax^2 - 2ax + a^2 - 1 = 0\) has exactly one real solution in \(x\).

\(a^2-1=(a+1)(a-1)\)

so the most likely possibilities are

\([x-(a+1)]^3\\ [x+(a+1)]^3\\ [x-(a-1)]^3\\ [x+(a+1)]^3\\ \)

I'd eliminate the last one becasue there won't be any minus signs.

I'd test the others.