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Math Help - Help with Polynomials and Radicals

  1. #1
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    Help with Polynomials and Radicals

    I am confused about the following problem, and cannot figure out how to solve it without using a graphing calculator.

    Sqrt(x+5) - Sqrt(2x+3) = -2

    How does one solve such a problem?
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  2. #2
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    Re: Help with Polynomials and Radicals

    Square both sides. You'll still have a radical on the LHS. Move everything but the radical term to the RHS, then square again. Should work.
    Last edited by zhandele; November 29th 2012 at 04:36 PM. Reason: correct mistake
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  3. #3
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    Re: Help with Polynomials and Radicals

    Ah. Thanks much.
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  4. #4
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    Re: Help with Polynomials and Radicals

    What answer did you get?
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  5. #5
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    Re: Help with Polynomials and Radicals

    Hello, yewchung!

    I tried the problem and got clumsy answers, but they checked out.
    (Well, one of them checked . . . the other was extraneous.)


    \text{Solve for }x\!:\;\sqrt{x+5} - \sqrt{2x+3} \:=\: -2

    Isolate a radical: . \sqrt{2x+3} \:=\:\sqrt{x+5} + 2

    Square both sides: . \left(\sqrt{2x+3}\right)^2 \;=\;\left(\sqrt{x+5}+2\right)^2

    n . . . . . . . . . . . . . . . . . 2x + 3 \;=\;x+5 + 4\sqrt{x+5} + 4

    Isolate the radical: . . . . . x - 6 \;=\;4\sqrt{x+5}

    Square both sides: . . . (x -6)^2 \;=\;\left(4\sqrt{x+5}\right)^2

    n . . . . . . . . . . . x^2 - 12x + 36 \;=\;16(x+5)

    n . . . . . . . . . . . x^2 - 12x + 36 \;=\;16x + 80

    n . . . . . . . . . . . x^2 - 28x - 44 \;=\;0

    Quadratic Formula: . x\;=\;\frac{28\pm\sqrt{960}}{2} \;=\;\frac{28\pm8\sqrt{15}}{2} \;=\;14 \pm4\sqrt{15}


    The only root is: . x \;=\;14 + 4\sqrt{15} \;=\;29.491933385\hdots
    Thanks from yewchung
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  6. #6
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    Re: Help with Polynomials and Radicals

    Thank you very much.
    Knowing my teacher, that clumsy number is probably the right one.
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