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Math Help - Equations

  1. #1
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    Equations

    Find all real solutions for

    sqrt(2x+11) - sqrt(2x-5) = 2

    Im not sure of how to do this question.. could someone help pleasee???
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  2. #2
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    Quote Originally Posted by fvaras89 View Post
    Find all real solutions for

    sqrt(2x+11) - sqrt(2x-5) = 2

    Im not sure of how to do this question.. could someone help pleasee???
    1. Determine the domain. With your question x \geq \frac52

    2. Isolate the roots:

    \sqrt{2x+11} = 2+\sqrt{2x-5}

    3. Square both sides:

    2x+11 = 4+ 2 \cdot 2 \cdot \sqrt{2x-5} +2x-5

    4. Isolate the root .... square both sides of the equation ... isolate the root ... etc until there aren't any roots left. You finally get:

    9 = 2x-5

    Solve for x.

    5. Since squaring is not an equivalent transformation you must check if you got a valid solution: Plug in the value for x into the original equation and check if you get a true statement.
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  3. #3
    Senior Member pacman's Avatar
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    i let y = sqrt(2x+11) - sqrt(2x-5) - 2, see my plot it may help you guess the answer
    Attached Thumbnails Attached Thumbnails Equations-plot.gif  
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