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IF $x , y , z$ are arbitary positive real numbers satisfying the equation

$$ 4xy + 6yz + 8xz = 9$$

Find the maximum value of the product $xyz$.

I dont know from where to begin .

3 variables and one equation.

How I can achieve this?

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    Are you familiar with lagrange multipliers? I'm guessing not because of the tag, but just checking2012-03-06
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    Lagrange Multipliers for constrained extremal points.2012-03-06
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    @Alex Becker No.I am not aware of lagrange multipliers.If it is something related to my question.Please let me know2012-03-06
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    @vikiiii It's a technique used in calculus for exactly this kind of problem.2012-03-06
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    @Alex how i can get to my answer?2012-03-06
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    This is the same sort of problem as the one in [this other question](http://math.stackexchange.com/questions/117000/find-the-maximum-possible-value-of-the-equation) of yours. The Wikipedia article on [Lagrange multipliers](http://en.wikipedia.org/wiki/Lagrange_multiplier) shows you how to solve these; it has some worked out examples.2012-03-06

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