Trey, Amelia, and Cho are discussing the solution set to the equation x^2 + 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?
Amelia
Cho
Trey
None of them are correct.

Answer 1

To find the correct solution to the equation \( x^2 + 9 = 45 \), we first need to solve for \( x \).

1. Start by isolating \( x^2 \): \[ x^2 + 9 = 45 \] Subtract 9 from both sides: \[ x^2 = 45 - 9 \] \[ x^2 = 36 \]

2. Next, take the square root of both sides: \[ x = \pm \sqrt{36} \] Which gives us: \[ x = 6 \quad \text{or} \quad x = -6 \]

Thus, the solution set is \( {-6, 6} \).

Now, let's evaluate the given statements:

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

The person who has found the correct solution set is Amelia.