Which of the following equations has only one solution: x² – 4x + 4 = 0, x² + x = 0, or x² – 1 = 0?

To determine which of the given equations has only one solution, we need to analyze each equation individually and look for their discriminants.

1. x² – 4x + 4 = 0: This is a perfect square trinomial. We can rewrite it as (x – 2)² = 0. The solution is x = 2, which is a repeated root. Thus, this equation has only one solution.
2. x² + x = 0: Factoring gives us x(x + 1) = 0, which results in two solutions: x = 0 and x = -1. So, this equation has two solutions.
3. x² – 1 = 0: This can be factored as (x – 1)(x + 1) = 0, yielding two solutions: x = 1 and x = -1. Therefore, this equation also has two solutions.

In conclusion, the equation x² – 4x + 4 = 0 has only one solution, which is x = 2.