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15 November, 11:20

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

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Answers (2)
  1. 15 November, 11:29
    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.
  2. 15 November, 11:40
    0
    The answer is a, x is 0
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