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Math Help - Inequality

  1. #1
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    Inequality

    would be nice if I could get some help with this.
    Inequality-ine.jpg
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  2. #2
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    Re: Inequality

    Try dividing both sides by the left-hand-side, so it looks like 1 < (3-sqrt(5))^....

    Note that 3-sqrt(5) is positive, so the inequality doesn't change when you divide by it, or any power of it. Also, being positive, those exponents are well defined for all x (well, except where x = -1 or x = 1, but that's assumed in writing the problem).

    Also note that 3-sqrt(5) < 1. This will effect how it behaves when you raise it to a power.
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  3. #3
    MHF Contributor MarkFL's Avatar
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    Re: Inequality

    Since 3-\sqrt{5}<1 the inequality implies:

    \frac{x-1}{x+1}<\frac{x+1}{x-1}
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