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

Trey
Trey

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

Amelia
Amelia

Cho

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

Thus, the solutions to the equation are \( -6 \) and \( 6 \).

Now, examining the options:

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

Therefore, Amelia has found the correct solution set.

The answer is: Amelia