document.write( "Question 269624: The difference of the reciprocals of two consecutive integers is 1/42. Find the integers. \n" ); document.write( "

Algebra.Com's Answer #197602 by drk(1908) $\"\"$ $\"About$

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we have
\n" ); document.write( "(i) $\"1%2Fx+-+1%2F%28x%2B1%29+=+1%2F42\"$
\n" ); document.write( "simplify the left side to get
\n" ); document.write( "(ii) $\"%281%29%2F%28x%28x%2B1%29%29+=+1%2F42\"$
\n" ); document.write( "cross multiply to get
\n" ); document.write( "(iii) $\"42+=+x%5E2+%2B+x\"$
\n" ); document.write( "set = 0 to get
\n" ); document.write( "(iv) $\"x%5E2+%2B+x+-42+=+0\"$
\n" ); document.write( "factoring, we get
\n" ); document.write( "(v) $\"%28x%2B7%29%28x-6%29+=+0\"$
\n" ); document.write( "So, x = -7 or x = 6
\n" ); document.write( "If x = -7 then x + 1 = -6 and we get -1/7 - (-1/6) = -1/7 + 1/6 = 1/42
\n" ); document.write( "If x = 6 then x + 1 = 7 and we get 1/6 - 1/7 = 1/42 \n" ); document.write( "

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