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

Cho
Cho

None of them are correct.
None of them are correct.

Amelia
Amelia

Trey

Answer 1

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

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

2. Next, we take the square root of both sides: \[ x = \pm 6 \]

This gives us two solutions: \( x = 6 \) and \( x = -6 \). Therefore, the solution set is \( {-6, 6} \).

Now let's compare the responses:

• Trey claims the solution is \( {6} \) (incomplete).
• Amelia correctly states the solution as \( {-6, 6} \).
• Cho states the solution as \( {-6} \) (incomplete).

Since Amelia provided the correct solution set, the answer is:

Amelia