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

Cho
Cho

Amelia
Amelia

None of them are correct.

Answer 1

To solve the equation \( x^2 + 9 = 45 \), we need to 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 \( x = -6 \).

Now, let's check each person's response:

• Trey says the solution is {6}, which is only one of the solutions.
• Amelia says the solution is {−6, 6}, which includes both solutions.
• Cho says the solution is {−6}, which is only one of the two solutions.

The correct solution set is {−6, 6}, which means Amelia has found the correct solution set.

Thus, the answer is Amelia.