document.write( "Question 821763: If the product of two positive numbers is 8 and their sum is 6, find the sum of their reciprocals \n" ); document.write( "
Algebra.Com's Answer #494404 by LinnW(1048)\"\" \"About 
You can put this solution on YOUR website!
let n = first number
\n" ); document.write( " m = second number
\n" ); document.write( "(n)(m) = 8
\n" ); document.write( " n + m = 6
\n" ); document.write( "Solve for n in the equation n + m = 6
\n" ); document.write( " n + m = 6
\n" ); document.write( "subtract m from each side.
\n" ); document.write( " n = 6 - m
\n" ); document.write( "substitute ( 6 - m ) in (n)(m) = 8
\n" ); document.write( " ( 6 - m )(m) = 8
\n" ); document.write( "distribute
\n" ); document.write( " 6m - m^2 = 8
\n" ); document.write( "subtract 8 from each side and reorder
\n" ); document.write( " -m^2 + 6m - 8 = 0
\n" ); document.write( "multiply by -1
\n" ); document.write( " m^2 - 6m + 8 = 0
\n" ); document.write( "factor
\n" ); document.write( " (m - 2)(m - 4) = 0
\n" ); document.write( "So m = 2 or m = 4\r
\n" ); document.write( "\n" ); document.write( "Since n = 6 - m
\n" ); document.write( " for m = 2 , n = 4
\n" ); document.write( " for m = 4 , n = 2\r
\n" ); document.write( "\n" ); document.write( "So one way or the other we end up with the two numbers 2 and 4.
\n" ); document.write( "The sum of their reciprocals is 1/2 + 1/4 = 3/4 \n" ); document.write( "
\n" );