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Find the greatest value of xyz for positive value of x,y,z subject to the condition yz+zx+xy=12
Solution: Given , $yz+zx+xy=12 (constant )$ ,the value of

$(yz)(zx)(xy)$ is greatest when

$yz=zx=xy$

Here ,   $n=3$ and $k=12$

Hence ,greatest value of   $(yz)(zx)(xy)$ is   $(frac123)^3=64.$

$herefore$ Greatest value of   $x^2y^2z^2$ is   $64.$

Thus ,greatest value of $xyz$ is $8.$ $8.$

Solution: Given , $yz+zx+xy=12 (constant )$ ,the value of

$(yz)(zx)(xy)$ is greatest when

$yz=zx=xy$

Here ,   $n=3$ and $k=12$

Hence ,greatest value of   $(yz)(zx)(xy)$ is   $(frac123)^3=64.$

$herefore$ Greatest value of   $x^2y^2z^2$ is   $64.$

Thus ,greatest value of $xyz$ is $8.$ $8.$

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