What is the solution of sqrt (2x+4) - sqrt (x) = 2 A. x = 0 B. x = 0 and x = 16 C. x = 0 and x = - 16 D. x = 16 and x = - 16

The answer is a, x is 0

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.