document.write( "Question 261753: Find two non negative numbers whose sum is 20 and for which the product of twice one number and the square of the other number will be a maximum. \n" ); document.write( "

Algebra.Com's Answer #192922 by drk(1908) $\"\"$ $\"About$

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Let A and B be the two non negative numbers.
\n" ); document.write( "(i) $\"A+%2B+B+=+20\"$
\n" ); document.write( "(ii) $\"2A+%2A+B%5E2+=+max\"$
\n" ); document.write( "step 1 - solve for A to get
\n" ); document.write( "(iii) $\"A+=+20+-+B\"$
\n" ); document.write( "step 2 - substitute (ii) into (i) to get
\n" ); document.write( "(iv) $\"2%2820-B%29+%2A+B%5E2\"$
\n" ); document.write( "step 3 - simplified we get
\n" ); document.write( "(v) $\"-2B%5E3+%2B+40B%5E2\"$
\n" ); document.write( "step 4 - take a derivative and set = 0 to get
\n" ); document.write( "(vi) $\"%28-6B%5E2%2B80B%29+=+0\"$
\n" ); document.write( "step 5 - factor to get
\n" ); document.write( "(vii) $\"%28-2B%283B+-+40%29%29+=+0\"$
\n" ); document.write( "We get
\n" ); document.write( "B = 0 or B = 13.3333
\n" ); document.write( "The closest integer to this is
\n" ); document.write( "B =13
\n" ); document.write( "so A = 7.
\n" ); document.write( "--
\n" ); document.write( "7+13 = 20
\n" ); document.write( "2*7 * 13^2 = 2366 \n" ); document.write( "

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