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

Cho
Cho

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

Trey
Trey
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Answer 1

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

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

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

This means the solutions are \( x = 6 \) and \( x = -6 \). Therefore, the solution set is \( {-6, 6} \).

Amelia is the only one who provides the correct solution set as {−6, 6}.

So, the correct answer is:

Amelia