document.write( "Question 357839: Find two real numbers whose sum is 18 and whose product is a minimum? \n" ); document.write( "

Algebra.Com's Answer #255549 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let the two numbers be X and Y.
\n" ); document.write( " $\"X%2BY=18\"$
\n" ); document.write( " $\"Y=18-X\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"P=X%2AY=X%2A%2818-X%29=18X-X%5E2\"$
\n" ); document.write( "To find the min or max of a quadratic, convert to vertex form.
\n" ); document.write( " $\"P=-X%5E2%2B18X=-%28X%5E2-18X%29\"$
\n" ); document.write( " $\"P=-X%5E2%2B18X=-%28X%5E2-18X%2B81%29%2B81\"$
\n" ); document.write( " $\"P=-X%5E2%2B18X=-%28X-9%29%5E2%2B81\"$
\n" ); document.write( "The min occurs at $\"X=9\"$ and equals
\n" ); document.write( " $\"P%5Bmin%5D=81\"$
\n" ); document.write( " \n" ); document.write( "

\n" );