Question

Question Trey, Amelia, and Cho are discussing the solution set to the equation x2+9=45 . Trey says the solution is {6} . Amelia says the solution is {−6,6} . Cho says the solution is {−6} . Which person has found the correct solution set? (1 point) Responses Trey Trey Amelia Amelia None of them are correct. None of them are correct. Cho

Answer 1

To solve the equation \( x^2 + 9 = 45 \), we start by isolating \( x^2 \):

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

2. Now, take the square root of both sides:
\[
x = \pm \sqrt{36}
\]
\[
x = \pm 6
\]

Thus, the solutions are \( -6 \) and \( 6 \).

Now, let's review what each person said:
- Trey said the solution is \{6\}, which is incorrect because it does not include \( -6 \).
- Amelia said the solution is \{-6, 6\}, which is correct.
- Cho said the solution is \{-6\}, which is incorrect because it does not include \( 6 \).

Therefore, the person who has found the correct solution set is **Amelia**.