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