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Thread: Ratio-inequation

  1. July 15th 2009, 10:39 PM #1
    dhiab
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    Ratio-inequation

    Solve in R :
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  2. July 15th 2009, 11:46 PM #2
    red_dog
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    The inequality is equivalent to \frac{x^2-4x-4}{x^2+4x-4}\geq 0

    <br /> \begin{array}{c | c c c c c c c c c c c}<br /> x & -\infty & -2-2\sqrt{2} & 2-2\sqrt{2} & -2+2\sqrt{2} & 2+2\sqrt{2} & \infty\\\hline\<br /> x^2-4x-4 & + & + & +0- & - & -0+ & +\\\hline<br /> x^2-4x-4 & + & +0- & - & -0+ & + & +\\\hline<br /> E(x) & + & +|- & -0+ & +|- & -0+ & +\\<br /> \end{array}<br />

    Then x\in(-\infty,-2-2\sqrt{2})\cup[2-2\sqrt{2},-2+2\sqrt{2})\cup[2+2\sqrt{2},\infty)
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