document.write( "Question 370862: The difference of the reciprocals of two consecutive integers is 1/72. Find the integers. \n" ); document.write( "

Algebra.Com's Answer #264313 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The difference of the reciprocals of two consecutive integers is 1/72.
\n" ); document.write( " Find the integers.
\n" ); document.write( ":
\n" ); document.write( "Two integers, x, (x+1)
\n" ); document.write( ":
\n" ); document.write( " $\"1%2Fx\"$ - $\"1%2F%28%28x%2B1%29%29\"$ = $\"1%2F72\"$
\n" ); document.write( "Multiply by 72x(x+1)
\n" ); document.write( "results:
\n" ); document.write( "72(x+1) - 72x = x(x+1)
\n" ); document.write( ":
\n" ); document.write( "72x + 72 - 72x = x^2 + x
\n" ); document.write( "72x's cancel, a quadratic equation
\n" ); document.write( "x^2 + x - 72 = 0
\n" ); document.write( "Factor this to
\n" ); document.write( "(x+9)(x-8) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "x = -9, -8
\n" ); document.write( "and
\n" ); document.write( "x = +8, 9 \n" ); document.write( "

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