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?

Answer 1

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

1. Subtract 9 from both sides: \[ x^2 = 45 - 9 \] \[ x^2 = 36 \]

2. Now, take the square root of both sides: \[ x = \pm \sqrt{36} \] \[ x = \pm 6 \]

This gives us two solutions: \( x = 6 \) and \( x = -6 \).

Now, let's evaluate what each person said:

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

Since the correct solution set is \( {-6, 6} \), Amelia has found the correct solution set.