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