Question

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

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

Amelia
Amelia

Cho
Cho

None of them are correct.
None of them are correct.
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Answer 1

To solve the equation \( x^2 + 9 = 45 \), we first need to 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:
\[
x = \pm 6
\]

This means that the solutions are \( x = 6 \) and \( x = -6 \).

Now, let's evaluate the claims:

- **Trey** says the solution is {6}. (Incorrect, as it misses -6.)
- **Amelia** says the solution is {−6, 6}. (Correct, includes both solutions.)
- **Cho** says the solution is {−6}. (Incorrect, as it misses 6.)

Thus, the person who has found the correct solution set is:

**Amelia**.