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 Amelia Amelia Trey Trey None of them are correct. None of them are correct. Cho

Answer 1

To solve the equation \( x^2 + 9 = 45 \), we start by isolating \( x^2 \):

\[ x^2 + 9 = 45 \]

Subtracting 9 from both sides:

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

Next, we take the square root of both sides to find \( x \):

\[ x = \pm \sqrt{36} \] \[ x = \pm 6 \]

This gives us the solutions \( x = 6 \) and \( x = -6 \). Thus, the solution set is:

\[ {-6, 6} \]

Amelia is correct in stating that the solution set is \({-6, 6}\). Therefore, the answer is:

Amelia.