document.write( "Question 348454: please help me to solve this problem. \"Find two real numbers whose sum is 18 and whose product is a minimum.\" tnx \n" ); document.write( "

Algebra.Com's Answer #249099 by Fombitz(32388) $\"\"$ $\"About$

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$\"A%2BB=18\"$
\n" ); document.write( "THe product is,
\n" ); document.write( " $\"P=A%2AB\"$
\n" ); document.write( "SUbsitute from above,
\n" ); document.write( " $\"A=18-B\"$
\n" ); document.write( " $\"P=%2818-B%29B=18B-B%5E2\"$
\n" ); document.write( "To find the maximum, convert to vertex form, $\"y=a%28x-h%29%5E2%2Bk\"$ , since the maximum occures at the vertex (h,k).
\n" ); document.write( "Complete the square to convert to vertex form,
\n" ); document.write( " $\"P=-%28B%5E2-18B%29\"$
\n" ); document.write( " $\"P=-%28B%5E2-18B%2B81%29%2B81\"$
\n" ); document.write( " $\"P=-%28B-9%29%5E2%2B81\"$
\n" ); document.write( "The maximum occurs at B=9, when A=9, and P=81. \n" ); document.write( "

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