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I've tried unsuccessfully to solve these two problems. I'd grateful for any help here.

  1. What is the biggest real number $z$ that obeys these two conditions: $$x + y + z=5 \quad\text{and}\quad xy +xz + yz=3\quad\text{?}$$
  2. Find the lower positive number for $$xy + 2xz + 3yz$$ if $xyz =48$.
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    What level are we talking about? Calculus, algebra? Is there a specific method you are expected to use? (E.g., the first problem can be solved in several ways, Lagrange multipliers among them).2011-04-14
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    @tom: It seems you have received useful answers to at least some of your questions. Please accept the ones you like by clicking the gray checkmark to the left.2011-04-14
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    If they are homework, they seem standard problems of Lagrange multipliers.2011-04-14
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    I'm just a high school student, so I think the simplest method. I suppose that it could be solved by arithmetic but I'm not completely sure of that.2011-04-14
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    @tom Please add and state what $x$, $y$ and $z$ are. Complex numbers? Real numbers? Positive real numbers? Please state!!2011-04-14
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    @David Benjamim Lim Well, I got that exercise like I wrote before.In the first exercise the numbers are real, as I said, and in the second one they are real as well.2011-04-15

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