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)
The correct solution set is Amelia's solution, which is {−6,6}.
To find the solution set to the equation x^2 + 9 = 45, we need to solve for x.
Starting with the equation:
x^2 + 9 = 45
Subtracting 9 from both sides:
x^2 = 36
Taking the square root of both sides:
√(x^2) = ±√36
Simplifying:
x = ±6
So the correct solution set is {-6, 6}.
Therefore, Amelia is correct and she has found the correct solution set.
To determine who has found the correct solution set, let's solve the equation x^2 + 9 = 45 step by step.
Step 1: Subtract 9 from both sides of the equation:
x^2 + 9 - 9 = 45 - 9
x^2 = 36
Step 2: Take the square root of both sides of the equation (remembering to include both positive and negative roots):
√(x^2) = ±√36
x = ±6
So, the correct solution set is {−6, 6}. Both Trey and Amelia have suggested this solution set, while Cho has only suggested {−6}. Therefore, the person who has found the correct solution set is Trey and Amelia.