Question

Trey, Amelia, and Cho are discussing the solution set to the equation x^2+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

Amelia
Amelia

Trey
Trey

Cho
Cho

None of them are correct.

Answer 1

To solve the equation \( x^2 + 9 = 45 \), we first subtract 9 from both sides:

\[
x^2 + 9 - 9 = 45 - 9
\]

This simplifies to:

\[
x^2 = 36
\]

Next, we take the square root of both sides. Remember that when you take the square root, you must consider both the positive and negative roots:

\[
x = \pm 6
\]

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

Now, let's analyze each person's claim:

- **Trey's solution**: {6} (only one solution, which is incorrect)
- **Amelia's solution**: {−6, 6} (includes both correct solutions)
- **Cho's solution**: {−6} (only one solution, which is incorrect)

From this, we can see that Amelia is the only one who provided the correct solution set.

Therefore, the correct answer is:

**Amelia**.