Question

Trey, Amelia, and Cho are discussing the solution set to the equation x^2+9=45. Trey says the solution is \left\{6\right\}. Amelia says the solution is \left\{-6,6\right\}. Cho says the solution is \left\{-6\right\}. Which person has found the correct solution set? (1 point) Responses None of them are correct. None of them are correct. Cho Cho Trey Trey Amelia

Answer 1

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

\[
x^2 + 9 = 45
\]
Subtracting 9 from both sides, we get:

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

Next, we take the square root of both sides:

\[
x = \pm \sqrt{36}
\]
\[
x = \pm 6
\]

This means the solutions are \(6\) and \(-6\).

Now let's compare this with what each person said:
- Trey said the solution is \(\{6\}\).
- Amelia said the solution is \(\{-6, 6\}\).
- Cho said the solution is \(\{-6\}\).

The correct solution set is \(\{-6, 6\}\), which matches Amelia's answer.

Therefore, the correct response is:

**Amelia**