document.write( "Question 569673: The sum of reciprocals of two consecutive even numbers is 5/12,find the numbers. \n" ); document.write( "

Algebra.Com's Answer #367441 by htmentor(1343) $\"\"$ $\"About$

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The sum of reciprocals of two consecutive even numbers is 5/12,find the numbers.
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\n" ); document.write( "Let n = the smaller number
\n" ); document.write( "Then n+2 = the other number
\n" ); document.write( "Given: sum of the reciprocals is 5/12
\n" ); document.write( "1/n + 1/(n+2) = 5/12
\n" ); document.write( "((n+2)+n)/(n(n+2)) = 5/12
\n" ); document.write( "Cross-multiply and collect terms:
\n" ); document.write( "12(2n+2) = 5n(n+2)
\n" ); document.write( "This gives 5n^2 - 14n - 24 = 0
\n" ); document.write( "This expression can be factored as
\n" ); document.write( "(5n+6)(n-4) = 0
\n" ); document.write( "This gives n = -6/5 [not an integer] and n = 4
\n" ); document.write( "So the two numbers are 4 and 6
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