To solve the equation \( x^2 + 9 = 45 \), we first subtract 9 from both sides:
\[ x^2 + 9 - 9 = 45 - 9 \]
This simplifies to:
\[ x^2 = 36 \]
Next, we take the square root of both sides. Remember that when you take the square root, you must consider both the positive and negative roots:
\[ x = \pm 6 \]
This means the solutions to the equation are \( x = 6 \) and \( x = -6 \).
Now, let's analyze each person's claim:
- Trey's solution: {6} (only one solution, which is incorrect)
- Amelia's solution: {−6, 6} (includes both correct solutions)
- Cho's solution: {−6} (only one solution, which is incorrect)
From this, we can see that Amelia is the only one who provided the correct solution set.
Therefore, the correct answer is:
Amelia.