document.write( "Question 362359: Find two numbers (exactly) whose product is 54 and whose sum is 23. \n" ); document.write( "

Algebra.Com's Answer #258235 by Fombitz(32388) $\"\"$ $\"About$

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Let A and B be the two numbers.
\n" ); document.write( "1. $\"A%2AB=54\"$
\n" ); document.write( "2. $\"A%2BB=23%7D%7D%0D%0AFrom+eq.+2%2C%0D%0A%7B%7B%7BA=23-B\"$
\n" ); document.write( "Substitute into eq. 1,
\n" ); document.write( " $\"%2823-B%29B=54\"$
\n" ); document.write( " $\"23B-B%5E2=54\"$
\n" ); document.write( " $\"B%5E2-23B%2B54=0\"$
\n" ); document.write( "Use the quadratic formula,
\n" ); document.write( " $\"B+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"B+=+%2823+%2B-+sqrt%28+%28-23%29%5E2-4%2A1%2A%2854%29+%29%29%2F%282%2A1%29+\"$
\n" ); document.write( " $\"highlight%28B+=+%2823+%2B-+sqrt%28+313%29%29%2F%282%29%29+\"$
\n" ); document.write( "Then
\n" ); document.write( " $\"A%2BB=23\"$
\n" ); document.write( " $\"A%2B%2823+%2B-+sqrt%28313%29%29%2F2=46%2F2\"$
\n" ); document.write( " $\"A=%2823+%2B-+sqrt%28313%29%29%2F2\"$
\n" ); document.write( ".
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\n" ); document.write( "(A,B)=( $\"%2823+-+sqrt%28313%29%29%2F2\"$ , $\"%2823+%2B+sqrt%28313%29%29%2F2\"$ )
\n" ); document.write( "and
\n" ); document.write( "(A,B)=( $\"%2823+%2B+sqrt%28313%29%29%2F2\"$ , $\"%2823+-+sqrt%28313%29%29%2F2\"$ )
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