Question

Trey, Amelia, and Cho are discussing the solution set to the equation x2+9=45.%0D%0A%0D%0ATrey says the solution is {6}.%0D%0A%0D%0AAmelia says the solution is {−6,6}.%0D%0A%0D%0ACho says the solution is {−6}.%0D%0A%0D%0AWhich person has found the correct solution set?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AAmelia%0D%0AAmelia%0D%0A%0D%0ACho%0D%0ACho%0D%0A%0D%0ATrey%0D%0ATrey%0D%0A%0D%0ANone of them are correct.%0D%0ANone of them are correct.

Answer 1

To solve the equation \( x^2 + 9 = 45 \), we first isolate \( x^2 \):

\[ x^2 = 45 - 9 \] \[ x^2 = 36 \]

Next, we 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 \( {-6, 6} \).

Now we can evaluate the responses:

• Trey says the solution is {6}. (Incorrect)
• Amelia says the solution is {-6, 6}. (Correct)
• Cho says the solution is {-6}. (Incorrect)

The correct answer is Amelia.