document.write( "Question 125400: The sum of the reciprocals of two consecutive even number is 7/24. Find the number...I can't figure out how to do this problem \n" ); document.write( "

Algebra.Com's Answer #91897 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"n\"$ is the 1st number
\n" ); document.write( " $\"n+%2B+2\"$ is the 2nd number
\n" ); document.write( " $\"%281+%2F+n%29+%2B+%281+%2F+%28n+%2B+2%29%29+=+7%2F24\"$
\n" ); document.write( "multiply both sides by $\"n%2A%28n%2B2%29\"$
\n" ); document.write( " $\"%28n+%2B+2%29+%2B+n+=+%287%2F24%29%2An%2A%28n+%2B+2%29\"$
\n" ); document.write( "multiply both sides by 24
\n" ); document.write( " $\"24%2A%282n+%2B+2%29+=+7n%5E2+%2B+14n\"$
\n" ); document.write( " $\"48n+%2B+48+=+7n%5E2+%2B+14n\"$
\n" ); document.write( " $\"7n%5E2+-+34n+-+48+=+0\"$
\n" ); document.write( " $\"%287n+%2B+8%29%28n+-+6%29+=+0\"$
\n" ); document.write( " $\"n+=+-%288%2F7%29\"$
\n" ); document.write( "I reject this since it's not a whole number and negative
\n" ); document.write( "and
\n" ); document.write( " $\"n+=+6\"$
\n" ); document.write( " $\"n+%2B+2+=+8\"$
\n" ); document.write( "The numbers are 6 and 8
\n" ); document.write( "check:
\n" ); document.write( " $\"%281%2F6%29+%2B+%281%2F8%29+=+7%2F24\"$
\n" ); document.write( "multiply both sides by 48
\n" ); document.write( " $\"8+%2B+6+=+14\"$
\n" ); document.write( " $\"14+=+14\"$
\n" ); document.write( "OK \n" ); document.write( "

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