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  4. Find the greatest value of xyz for positive values of x, y, z subject to the condition x y+ y z +z x=12 .

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Q. Find the greatest value of $xyz$ for positive values of $x, y, z$ subject to the condition $x y+ y z +z x=12$ .

ManipalManipal 2013

Solution:

By hit and trial method taking $x=y=z=2$,
we get $x y +y z +z x=12$
and $x y z=8$.