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Math Help - proving

  1. #1
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    Post proving

    how can i do
    (a+b+c)(1/a + 1/b + 1/c)>= 9

    is there any theorem to use?
    i dont know theorems based on this..
    can u help me with this?
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  2. #2
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    Quote Originally Posted by nh149 View Post
    how can i do
    (a+b+c)(1/a + 1/b + 1/c)>= 9

    is there any theorem to use?
    i dont know theorems based on this..
    can u help me with this?
    Without conditions on a, b and c this question makes no sense
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  3. #3
    J.R
    J.R is offline
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    actually, we must just precise that a, b , c are three positif reals not null.

    indeed, we can apply the Cauchy-Schwarz's inegalitie:

    we have directly:

    (\sqrt{a}^2+\sqrt{b}^2+\sqrt{c}^2)((\frac{1}{\sqrt  {a}})^2+(\frac{1}{\sqrt{b}})^2+(\frac{1}{\sqrt{c}}  )^2)\ge (1+1+1)^2=9

    cqfd

    @+
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