We want to solve
√(2x+4) - √(x) = 2
Write equation as
√(2x+4) = √x + 2
Square each side.
2x + 4 = x + 4√x + 4
x = 4√x
x - 4√x = 0
√x (√x - 4) = 0
Either
√x = 0 => x = 0
or
√x = 4 => x = 16
Test for extraneous solutions.
When x = 0:
√(2x+4) - √x = 2 (Correct)
When x = 16:
√(2x+4) - √x = √(36) - √(16) = 6 - 4 = 2 (Correct)
A plot of f(x) = √(2x+4) - √x - 2 = 0 confirms hat the solutions are correct.
Answer: B. x = 0 and x = 16.
√(2x+4) - √(x) = 2
Write equation as
√(2x+4) = √x + 2
Square each side.
2x + 4 = x + 4√x + 4
x = 4√x
x - 4√x = 0
√x (√x - 4) = 0
Either
√x = 0 => x = 0
or
√x = 4 => x = 16
Test for extraneous solutions.
When x = 0:
√(2x+4) - √x = 2 (Correct)
When x = 16:
√(2x+4) - √x = √(36) - √(16) = 6 - 4 = 2 (Correct)
A plot of f(x) = √(2x+4) - √x - 2 = 0 confirms hat the solutions are correct.
Answer: B. x = 0 and x = 16.