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Math Help - proving question

  1. #1
    Junior Member
    Joined
    Oct 2010
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    proving question

    Having trouble with this question, any help will be appreciated, thanks.
    Let x be a positive number, with  x^2>2.
    Let  y = x/2 + 1/x
    Show that  0<y<x, and that  y^2>2. Explain why this shows that there is no smallest positive number whoes square is more than 2.
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  2. #2
    MHF Contributor
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    Just do the claims in turn. To show that y < x, show that 1/x < x/2. To show y^2>2, calculate (x/2+1/x)^2. I hope you can figure out the last part provided the rest is shown.
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