document.write( "Question 431489: One number is 3 more than another number. The sum of their reciprocals is 1/2. what are the numbers? \n" ); document.write( "

Algebra.Com's Answer #299436 by josmiceli(19441) $\"\"$ $\"About$

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Call the numbers $\"a\"$ and $\"b\"$
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+=+b+%2B+3+\"$
\n" ); document.write( "(2) $\"+1%2Fa+%2B+1%2Fb+=+1%2F2+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "Multiply both sides of (2) by $\"2a%2Ab\"$
\n" ); document.write( "(2) $\"+2b+%2B+2a+=+a%2Ab+\"$
\n" ); document.write( "By substitution:
\n" ); document.write( "(2) $\"+2b+%2B+2%2A%28b+%2B+3%29+=+%28b+%2B+3%29%2Ab+\"$
\n" ); document.write( "(2) $\"+2b+%2B+2b+%2B+6+=+b%5E2+%2B+3b+\"$
\n" ); document.write( "(2) $\"+b%5E2+-+b+=+6+\"$
\n" ); document.write( "Complete the square
\n" ); document.write( " $\"+b%5E2+-+b+%2B+%281%2F2%29%5E2+=+6+%2B+%281%2F2%29%5E2+\"$
\n" ); document.write( " $\"+%28+b+-+1%2F2%29%5E2+=+24%2F4+%2B+1%2F4+\"$
\n" ); document.write( " $\"+%28+b+-+1%2F2%29%5E2+=+25%2F4+\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( " $\"+b+-+1%2F2+=+5%2F2+\"$
\n" ); document.write( " $\"+b+=+3+\"$ and also
\n" ); document.write( " $\"+b+-+1%2F2+=+-5%2F2+\"$
\n" ); document.write( " $\"+b+=+-2+\"$
\n" ); document.write( "And, from (1),
\n" ); document.write( "(1) $\"+a+=+-2+%2B+3+\"$
\n" ); document.write( " $\"+a+=+1+\"$
\n" ); document.write( "The numbers are 1 and -2
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"+1%2Fa+%2B+1%2Fb+=+1%2F2+\"$
\n" ); document.write( "(2) $\"+1%2F1+%2B+1%2F%28-2%29+=+1%2F2+\"$
\n" ); document.write( " $\"+1+-+1%2F2+=+1%2F2+\"$
\n" ); document.write( "OK \n" ); document.write( "

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