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

 Oct 8, 2022
 #2
avatar+118132 
+2

 

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

 

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.

 Oct 9, 2022

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