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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
The maximum value is 2%2A2%2A2%2A2%2A2=2%5E5=32 .
In two dimensions, for a fixed perimeter,
length%2Bwidth=perimeter%2F2 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 width%2Blength%2Bheight ,
and we are trying to make the cuboid box with the larges volume,
the best choice is a cube with width=length=height .
The same works for 5 positive numbers with a given sum:
the greatest product is obtained when all numbers are the equal.
So with a=b=c=d=e , a%2Bb%2Bc%2Bd%2Be=10 turns into
a%2Ba%2Ba%2Ba%2Ba=10 ---> 5a=10 ---> a=10%2F5 ---> a=2 .
Then a%2Ab%2Ac%2Ad%2Ae=2%2A2%2A2%2A2%2A2=2%5E5=32 .
The explanation your teacher wants depends on the level of your class.