Trey, Amelia, and Cho are discussing the solution set to the equation x2+9=45 .

To solve the equation \( x^2 + 9 = 45 \), we need to isolate \( x^2 \):

1. Subtract 9 from both sides:
\[
x^2 = 45 - 9
\]
\[
x^2 = 36
\]

2. Next, we take the square root of both sides:
\[
x = \pm 6
\]

This gives us two solutions: \( x = 6 \) and \( x = -6 \).

Now, let's check each person's response:

- Trey says the solution is {6}, which is only one of the solutions.
- Amelia says the solution is {−6, 6}, which includes both solutions.
- Cho says the solution is {−6}, which is only one of the two solutions.

The correct solution set is {−6, 6}, which means **Amelia** has found the correct solution set.

Thus, the answer is Amelia.