SOLUTION: a+b+c+d+e=10(all positive number),then maximum value of a*b*c*d*e is

SOLUTION: a+b+c+d+e=10(all positive number),then maximum value of abcde is

Question 880354: a+b+c+d+e=10(all positive number),then maximum value of a*b*c*d*e is
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The maximum value is .
In two dimensions, for a fixed perimeter,
is fixed,
the largest rectangle we can make is a square,
which has the same measurement for both dimensions: length = width.
In three dimensions, if we have a maximum (or a fixed value) for ,
and we are trying to make the cuboid box with the larges volume,
the best choice is a cube with .
The same works for 5 positive numbers with a given sum:
the greatest product is obtained when all numbers are the equal.
So with , turns into
---> ---> ---> .
Then .
The explanation your teacher wants depends on the level of your class.
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