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?
Amelia has found the correct solution set. The equation x^2 + 9 = 45 can be rewritten as x^2 = 36, which can be factored as (x-6)(x+6) = 0. This means that x = -6 or x = 6, so the correct solution set is {-6, 6}.
To determine who has found the correct solution set, we need to solve the equation and compare their solutions.
Given the equation x^2 + 9 = 45, we want to find the values of x that satisfy this equation.
Moving the constant term, 9, to the other side of the equation, we have x^2 = 45 - 9.
Simplifying further, we have x^2 = 36.
Taking the square root of both sides, we get x = ±√36.
Simplifying the square root of 36 gives us x = ±6.
Therefore, the correct solution set is {−6, 6}, as stated by Amelia.