Solve the radical equation Vx + 9 = × - 3. Check for extraneous solutions.

Answer 1

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.