Solve the radical equation
Vx - /49 - x = 7. Identify the
extraneous solution. Write your answers as reduced fractions, if
necessary
First, let's simplify the radical equation:
√(49 - x) = 7 + x
Square both sides to eliminate the radical:
49 - x = (7 + x)^2
49 - x = 49 + 14x + x^2
Rearrange the terms to get a quadratic equation:
x^2 + 15x = 0
Factor out x:
x(x + 15) = 0
So, x = 0 or x = -15
Now, let's check the solutions for the original equation to find the extraneous solution:
For x = 0:
√(49 - 0) = 7 + 0
√49 = 7
7 = 7 (true)
So, x = 0 is a valid solution.
For x = -15:
√(49 - (-15)) = 7 + (-15)
√64 = -8
8 = -8 (false)
So, x = -15 is the extraneous solution.
Therefore, the correct solution to the radical equation Vx - √(49 - x) = 7 is x = 0.