Question

Trey, Amelia, and Cho are discussing the solution set to the equation x2+9=45.%0D%0A%0D%0ATrey says the solution is {6}.%0D%0A%0D%0AAmelia says the solution is {−6,6}.%0D%0A%0D%0ACho says the solution is {−6}.%0D%0A%0D%0AWhich person has found the correct solution set?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AAmelia%0D%0AAmelia%0D%0A%0D%0ACho%0D%0ACho%0D%0A%0D%0ATrey%0D%0ATrey%0D%0A%0D%0ANone of them are correct.%0D%0ANone of them are correct.

Answer 1

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

\[
x^2 = 45 - 9
\]
\[
x^2 = 36
\]

Next, we take the square root of both sides:

\[
x = \pm 6
\]

This means the solutions are \( x = 6 \) and \( x = -6 \). Therefore, the solution set is \( \{-6, 6\} \).

Now we can evaluate the responses:

- Trey says the solution is \{6\}. (Incorrect)
- Amelia says the solution is \{-6, 6\}. (Correct)
- Cho says the solution is \{-6\}. (Incorrect)

The correct answer is **Amelia**.