document.write( "Question 472731: the sum of the reciprocals of two consecutive even integers is 10 times the reciprocal of their product. find these integers. \n" ); document.write( "

Algebra.Com's Answer #324162 by htmentor(1343) $\"\"$ $\"About$

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Let n and n+2 be the two consecutive even integers.
\n" ); document.write( "So we can write
\n" ); document.write( "1/n + 1/(n+2) = 10/(n(n+2))
\n" ); document.write( "The LCD of the LHS is n(n+2)
\n" ); document.write( "Since denominators are equal we can set the numerators equal:
\n" ); document.write( "(n+2) + n = 10
\n" ); document.write( "2n + 2 = 10
\n" ); document.write( "This gives n = 4
\n" ); document.write( "So the integers are 4 and 6 \n" ); document.write( "

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