Trey, Amelia, and Cho are discussing the solution set to the equation x2+9=45.

Question

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

Amelia
Amelia
None of them are correct.
None of them are correct.
Cho
Cho
Trey

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:

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

\[ x = \pm 6 \]

This means the solution set is \({-6, 6}\).

Among the responses:

• Trey says the solution is {6} - Incorrect.
• Amelia says the solution is {-6, 6} - Correct.
• Cho says the solution is {-6} - Incorrect.

Thus, the correct answer is:

Amelia.