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

Cho
Cho

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

Amelia

1 answer

Let's solve the equation \( x^2 + 9 = 45 \).

First, let's isolate \( x^2 \):

\[ x^2 + 9 = 45 \]

Subtract 9 from both sides:

\[ x^2 = 45 - 9 \]

\[ x^2 = 36 \]

Next, we take the square root of both sides:

\[ x = \pm6 \]

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

\[ {-6, 6} \]

Now let's evaluate the answers given by Trey, Amelia, and Cho:

  • Trey says the solution is \( {6} \) (incorrect).
  • Amelia says the solution is \( {-6, 6} \) (correct).
  • Cho says the solution is \( {-6} \) (incorrect).

Thus, the correct answer is Amelia.