Solve the radical equation Vx + 9 = × - 3. Check for extraneous solutions.
To solve the radical equation Vx + 9 = x - 3, we first need to isolate the radical term on one side of the equation.
Vx = x - 3 - 9
Vx = x - 12
Now, to get rid of the square root, square both sides of the equation:
(Vx)^2 = (x - 12)^2
x^2 = x^2 - 24x + 144
0 = -24x + 144
24x = 144
x = 144 / 24
x = 6
Therefore, the solution to the radical equation Vx + 9 = x - 3 is x = 6.
Now, we need to check for any extraneous solutions.
By plugging x = 6 back into the original equation:
V(6) + 9 = 6 - 3
3√6 + 9 = 3
3 + 9 = 6
12 = 6
Since 12 does not equal 6, there are no extraneous solutions.
Therefore, the solution to the radical equation Vx + 9 = x - 3 is x = 6.