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Math Help - proving

  1. #1
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    proving

    If p , q and r \in positive real numbers , with at least one of them less than unity , prove that (1-p)(1-q)(1-r)>1-p-q-r
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  2. #2
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    Quote Originally Posted by mathaddict View Post

    If p , q and r \in positive real numbers , with at least one of them less than unity , prove that (1-p)(1-q)(1-r)>1-p-q-r
    after expanding the LHS, your inequality becomes: pq+qr+rp > pqr. dividing by pqr gives us: \frac{1}{p}+\frac{1}{q}+\frac{1}{r} > 1, which is true because we have that at least one of \frac{1}{p}, \frac{1}{q}, \frac{1}{r} is bigger than 1.
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  3. #3
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    Quote Originally Posted by NonCommAlg View Post
    after expanding the LHS, your inequality becomes: pq+qr+rp > pqr. dividing by pqr gives us: \frac{1}{p}+\frac{1}{q}+\frac{1}{r} > 1, which is true because we have that at least one of \frac{1}{p}, \frac{1}{q}, \frac{1}{r} is bigger than 1.
    Thanks a lot , sorry for not posting this in my main post , what does "less than unity " mean , is it greater than 1 ?
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  4. #4
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    Quote Originally Posted by mathaddict View Post
    what does "less than unity " mean , is it greater than 1 ?
    Less than unity means less than 1. Unity = 1
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