document.write( "Question 880354: a+b+c+d+e=10(all positive number),then maximum value of a*b*c*d*e is \n" ); document.write( "

Algebra.Com's Answer #531453 by KMST(5328) $\"\"$ $\"About$

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The maximum value is $\"2%2A2%2A2%2A2%2A2=2%5E5=32\"$ .
\n" ); document.write( "In two dimensions, for a fixed perimeter,
\n" ); document.write( " $\"length%2Bwidth=perimeter%2F2\"$ is fixed,
\n" ); document.write( "the largest rectangle we can make is a square,
\n" ); document.write( "which has the same measurement for both dimensions: length = width.
\n" ); document.write( "In three dimensions, if we have a maximum (or a fixed value) for $\"width%2Blength%2Bheight\"$ ,
\n" ); document.write( "and we are trying to make the cuboid box with the larges volume,
\n" ); document.write( "the best choice is a cube with $\"width=length=height\"$ .
\n" ); document.write( "The same works for 5 positive numbers with a given sum:
\n" ); document.write( "the greatest product is obtained when all numbers are the equal.
\n" ); document.write( "So with $\"a=b=c=d=e\"$ , $\"a%2Bb%2Bc%2Bd%2Be=10\"$ turns into
\n" ); document.write( " $\"a%2Ba%2Ba%2Ba%2Ba=10\"$ ---> $\"5a=10\"$ ---> $\"a=10%2F5\"$ ---> $\"a=2\"$ .
\n" ); document.write( "Then $\"a%2Ab%2Ac%2Ad%2Ae=2%2A2%2A2%2A2%2A2=2%5E5=32\"$ .
\n" ); document.write( "The explanation your teacher wants depends on the level of your class. \n" ); document.write( "

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