document.write( "Question 143775: The sum of a number and its reciprocal is 13/6. What are the numbers?\r
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Algebra.Com's Answer #104656 by ptaylor(2198) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Let x=the number
\n" ); document.write( "Then 1/x= the reciprocal of the number\r
\n" ); document.write( "\n" ); document.write( "x+1/x=13/6 multiply each term by 6x\r
\n" ); document.write( "\n" ); document.write( "6x^2+6=13x subtract 13x from each side\r
\n" ); document.write( "\n" ); document.write( "6x^2-13x+6=0------------------quadratic in standard form. Solve using the quadratic formula:\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"x+=+%2813+%2B-+sqrt%28+13%5E2-4%2A6%2A6+%29%29%2F%282%2A6%29+\"$
\n" ); document.write( " $\"x+=+%2813+%2B-+sqrt%28+169-144%29%29%2F%2812%29+\"$
\n" ); document.write( " $\"x+=+%2813+%2B-+sqrt%2825%29%29%2F%2812%29+\"$
\n" ); document.write( " $\"x+=+%2813+%2B-5%29%2F%2812%29+\"$
\n" ); document.write( " $\"x+=+%2813-5%29%2F%2812%29=8%2F12=2%2F3+\"$ and
\n" ); document.write( " $\"x+=+%2813+%2B5%29%2F%2812%29=18%2F12+=3%2F2\"$
\n" ); document.write( "This tells us that the number can either be 2/3 or 3/2\r
\n" ); document.write( "\n" ); document.write( "CK\r
\n" ); document.write( "\n" ); document.write( "2/3+3/2=13/6
\n" ); document.write( "4/6+9/6=13/6
\n" ); document.write( "13/6=13/6\r
\n" ); document.write( "\n" ); document.write( "Hope this helps----ptaylor\r
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