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Thread: please solve

  1. #1
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    please solve

    Let S be a set of positive real numbers. If S contains at least four distinct elements show that there are elements x,y ∈ S such that
    $Given\ z(x,\ y) = \dfrac{x- y}{1 + xy}\ and\ x,\ y \in S,$

    $\text{where S is a set of at least 4 distinct positive real numbers}$

    $Prove\ \exists\ x,\ y \in\ S\ such\ that\ 0 < z(x,\ y) < \dfrac{\sqrt{3}}{3}.$


    What can you say if S has at least 7 elements? What if S has at least n elements, where n > 2?
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  2. #2
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    Re: please solve

    Hey pankajprithyani.

    Have you tried looking at setting x close to y where the numerator gets small and the denominator gets large? That will take the number down to a small value.
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  3. #3
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    Re: please solve

    I can't understand please explain

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